David Cameron has praised Barack Obama's "strength, moral authority and wisdom" as the pair reiterated their nations' "special relationship".
President Obama called the UK prime minister "the kind of partner you want at your side" as he welcomed him to his biggest White House state dinner yet.
On its star-studded 360-name guest list were actor George Clooney, golfer Rory McIlroy and Homeland star Damian Lewis.
Mr Cameron ends his three-day US trip by visiting Ground Zero on Thursday.
His itinerary for the day also includes visits to New York University, City Hall and a charter school - seen as the model for the free schools being introduced in the UK.
Wednesday had seen the leaders spend two hours in talks on issues such as Syria, Iran and the war in Afghanistan.
Speaking at a press conference afterwards, Mr Cameron said the mission in Afghanistan was moving into its "final phases".
Both leaders stressed that progress had been made in the country - despite the loss of US, British and Afghan lives.
Mr Obama confirmed international forces would take on a support role from 2013, with Afghans in full charge of security in 2014.
The UK prime minister also raised the issue of reviewing how extradition agreements were operating amid concerns US officials were having to produce less evidence than their British counterparts to support cases.
But at the state dinner the leaders returned to what has been a frequent theme during the visit - their countries' close relations - and spoke of their personal bond.
Mr Cameron praised the president for having "pressed the reset button on the moral authority of the entire free world".
Comparing Mr Obama to Theodore Roosevelt, Mr Cameron said he understood that "America must do the right thing but to provide moral leadership America must do it in the right way too".
He praised Mr Obama for being strong when required to defend US national interests, while not rushing to "pick fights", and for having "found a new voice for America with the Arab people".
"Barack, it is an honour to call you an ally, a partner and a friend," he added.
Likewise, Mr Obama said of the prime minister: "I trust him. He says what he does and he does what he says. I've seen his character. I've seen his commitment to human dignity during Libya."
The president also spoke of Mr Cameron and his wife Samantha having "shown a measure of strength that few of us will ever know", in a reference to the death of their eldest son, Ivan, at the age of six.
Guests at the White House dined on Bison Wellington, combining the classic British pastry-around-meat dish with North Dakota buffalo loin.
Several of those in attendance were said to be key donors to President Obama's re-election fund, such as movie mogul Harvey Weinstein.
Other notable guests included actors Hugh Bonneville and Elizabeth McGovern, from ITV period drama Downton Abbey, British Olympic heptathlon gold medallist Denise Lewis, and Virgin boss Sir Richard Branson.
Entertainment was provided by US R&B star John Legend and English folk-rock band Mumford & Sons - a favourite of Mrs Cameron.