(CNN) -- As reactions poured in from all over the world to the announcement that Osama bin Laden was killed in a U.S. operation, President Barack Obama declared it "a good day for America."
"Our country kept its commitment to see that justice is done," Obama said Monday. The world, he said, is a better place because of bin Laden's death, and the successful operation reminds Americans that there is "nothing we can't do" when they work together.
Noting that patriotic crowds have gathered across the country to celebrate, the president said, "We're reminded that we're fortunate to have Americans who have dedicated their lives to protecting ours."
"As commander-in-chief, I could not be prouder," Obama said at a previously scheduled Medal of Honor ceremony.
A DNA match confirms with virtual certainty that Osama bin Laden was killed in the operation, a senior administration official told CNN Monday. Officials compared DNA of the person killed with bin Laden "family DNA," a senior administration official said.
There are also photographs of the body with a gunshot wound to the side of the head that shows an individual who is recognizable as bin Laden, a U.S. government official said. No decision has yet been made on whether to release the photographs and if so, when and how.
One of bin Laden's wives identified the body to U.S. forces, a senior U.S. defense official said.
The mastermind of the September 11, 2001, terrorist attacks -- the worst terrorist attacks on American soil -- was killed by U.S. forces Monday in a mansion in Abbottabad, about 50 kilometers (30 miles) north of the Pakistani capital, Islamabad, U.S. officials said.
Four others in the compound also were killed. One of them was bin Laden's adult son, and another was a woman being used as a shield by a male combatant, the officials said.
A U.S. government official told CNN the operation that killed the founder and leader of al Qaeda was designed to do just that, not to take him alive. But another senior U.S. official told CNN the operation included instructions to arrest bin Laden alive if he surrendered -- however, no one involved expected that he would surrender.
Details of exactly how the raid played out have not been released.
In the operation, U.S. forces recovered "quite a bit of material," a senior U.S. intelligence official said. "There's a robust collection of materials we need to sift through, and we hope to find valuable intelligence that will lead us to other players in al Qaeda." A task force has been set up "because of the sheer volume of material collected," the official said. "That material is currently being exploited and analyzed."
The successful operation sends a message to the Taliban in Afghanistan, U.S. Secretary of State Hillary Clinton said Monday.
"You cannot wait us out. You cannot defeat us. But you can make the choice to abandon al Qaeda" and participate in a peaceful political process, Clinton said.
"There is no better rebuke to al Qaeda and its heinous ideology," she said. "The fight continues and we will never waver."
Some doubted that the terrorist leader would ever be caught, she said, but "this is America... We persevere, and we get the job done."
Clinton also noted that bin Laden's death comes at a time of "great movements toward freedom and democracy."
Bin Laden's body was later buried at sea, an official said. Many Muslims adhere to the belief that bodies should be buried within one day.
The official did not release additional details about the burial, but said it was handled in keeping with Muslim customs.
The death of the founder and leader of al Qaeda comes almost 10 years after the September 11, 2001, attacks. The announcement in the United States of bin Laden's death came on the same date -- May 1 -- that Adolf Hitler's death was announced in 1945.
Terrorists "almost certainly will attempt to avenge" the death of Osama bin Laden, CIA Director Leon Panetta said in a message sent to agency employees.
The operation was "CIA-driven," a senior administration official told CNN. Obama and Panetta considered all options, the source said.
Homeland Security Secretary Janet Napolitano, in a statement, said the "death of Osama bin Laden is an important success not only for the United States, but the entire world. Our efforts to combat terrorism, however, do not fixate on one individual, and we remain completely focused on protecting our nation against violent extremism of all kinds."
The Department of Homeland Security does not plan to issue a new alert, and would only do so if there is "specific or credible information to convey," she said. "... Our security posture, which always includes a number of measures both seen and unseen, will continue to respond appropriately to protect the American people from an evolving threat picture both in the coming days and beyond."
A Transportation Security Administration official said the TSA "continually evaluates the latest threats and screening measures which are implemented based on the latest intelligence."
U.S. diplomatic facilities around the world were placed on high alert following the announcement of bin Laden's death, a senior U.S. official said, and the U.S. State Department issued a "worldwide caution" for Americans.
The travel alert warned of the "enhanced potential for anti-American violence given recent counter-terrorism activity in Pakistan."
Among those who lost loved ones, there was a mix of celebration and remembrance. "While we can close the book on Osama bin Laden at present, for the parents and families there will never be closure," said Sally Regenhard, mother of a firefighter who died on 9/11, describing the day as "bittersweet."
"It's good to see an evil person receive justice," she added, "but it's very bitter to realize that so many good people met a brutal and needless death at the hands of this monster."
In an address to the nation Sunday night, Obama called bin Laden's death "the most significant achievement to date in our nation's effort to defeat al Qaeda." Washington is nine hours behind Pakistan.
"Today, at my direction, the United States launched a targeted operation against that compound in Abbottabad, Pakistan," Obama said. "A small team of Americans carried out the operation with extraordinary courage and capability. No Americans were harmed. They took care to avoid civilian casualties. After a firefight, they killed Osama bin Laden and took custody of his body."
A congressional source familiar with the operation said bin Laden was shot in the head.
The killing of bin Laden was the culmination of years of intelligence work and months of following a specific lead, senior U.S. administration officials said.
The key break involved one of the few couriers trusted by bin Laden, according to the officials. About two years ago, intelligence work identified where the courier and his brother lived and operated in Pakistan, and it took until August to find the compound in Abbottabad that was raided, they said.
According to the senior administration officials, intelligence work determined at the beginning of 2011 that bin Laden might be located at the compound.
Obama chaired five National Security Council meetings from mid-March until late April, with the last two on April 19 and April 28 -- last Thursday.
On Friday morning -- before visiting Alabama's tornado-ravaged areas -- Obama gave the order for the mission, the officials said.
Senior Obama administration officials believe the compound was built five years ago for the specific purpose of hiding bin Laden. U.S. forces carried out several so-called "practice runs" in order to minimize casualties.
Footage that aired Monday on CNN affiliate GEO TV showed fire and smoke spewing from the compound where bin Laden was killed.
One resident in the city of Lahore said Monday she was stunned to hear bin Laden was in the country.
"But was it really him?" the woman said.
A senior national security official told CNN that officials had multiple confirmations that the body was bin Laden's, saying they had the "ability to run images of the body and the face."
A resident in Abbottabad, who did not want to be fully identified, said he was wary of making any personal statements or giving his reaction to the news. But he said the house where bin Laden allegedly was killed has been occupied by many people for the past five years.
Half a world away, the scene outside the White House was one of pure jubilation.
Hundreds reveled through the night, chanting "USA! USA!" Others chanted "Hey, hey, hey, goodbye!" in reference to the demise of bin Laden. Many also spontaneously sang the national anthem.
In New York, a cheering crowd gathered at ground zero -- the site where the twin towers of the World Trade Center stood before bin Laden's terrorist group flew two planes into the buildings on September 11, 2001. Strains of "God Bless America" could be heard intermittently trickling through the crowd.
One former New York firefighter -- forced to retire due to lung ailments suffered as a result of the dust from ground zero -- said he was there to let the 343 firefighters who died in the attacks know "they didn't die in vain."
"It's a war that I feel we just won," he said. "I'm down here to let them know that justice has been served."
Bob Gibson, a retired New York police officer, said the news of bin Laden's death gave him a sense of "closure."
"I never thought this night would come, that we would capture or kill bin Laden," he said. "And thank the Lord he has been eliminated."
Bin Laden once reportedly slipped out of a training camp in Afghanistan just hours before a barrage of U.S. cruise missiles destroyed it.
He had been implicated in a series of deadly, high-profile attacks that had grown in their intensity and success during the 1990s. They included a deadly firefight with U.S. soldiers in Somalia in October 1993, the bombings of two U.S. embassies in East Africa that killed 224 in August 1998, and a bomb attack on the USS Cole that killed 17 sailors in October 2000.
In his speech Sunday night, Obama reiterated that the United States is not fighting Islam.
"I've made clear, just as President Bush did shortly after 9/11, that our war is not against Islam. Bin Laden was not a Muslim leader; he was a mass murderer of Muslims," Obama said.
The Council on American-Islamic Relations (CAIR), a Muslim civil rights and advocacy organization, welcomed the death of bin Laden.
"As we have stated repeatedly since the 9/11 terror attacks, bin Laden never represented Muslims or Islam. In fact, in addition to the killing of thousands of Americans, he and al Qaeda caused the deaths of countless Muslims worldwide," the statement said.
While the death of bin Laden "is a significant victory," the war on terrorism is not over, said Frances Fragos Townsend, former Homeland Security adviser to President George W. Bush.
"We've been fighting these fractured cells. We've seen the U.S. government, military and intelligence officials deployed around the world," Townsend said. "By no means are these other cells nearly as dangerous as he is, but we will continue to have to fight in chaotic places."
But for now, many Americans were soaking up the historic moment.
"It's what the world needed," said Dustin Swensson, a military veteran of the Iraq war who joined the revelers outside the White House. "(I'll) always remember where I was when the towers went down, and I'm always going to remember where I am now."