Kerry is visiting the city, which was obliterated by a U.S. atomic bomb on Aug. 6, 1945, to attend gathering of foreign ministers from the Group of Seven (G7) advanced economies that Japan opened on Sunday with a call to end nuclear weapons.
The U.S. diplomat is to join his counterparts from Britain, Canada, France, Germany, Italy and Japan on Monday to tour the city's atomic bomb museum and to lay flowers at a cenotaph for its victims, becoming the first in his post to do so.
"If you are asking whether the secretary of state came to Hiroshima to apologise, the answer is no," a senior U.S. official told reporters late on Sunday.
"If you are asking whether the secretary and I think all Americans and all Japanese are filled with sorrow at the tragedies that befell so many of our countrymen, the answer is yes," the official, who spoke on condition of anonymity, added.
Kerry's trip could pave the way for an unprecedented visit to Hiroshima by a sitting U.S. president when Barack Obama attends the annual G7 summit to be held in Japan next month.
While saying the White House has yet to make a decision, the senior U.S. official said Obama has shown he is willing to do controversial things such as visiting Havana last month.
The official suggested there was no "great or insurmountable angst about the optics or the politics of a visit to Hiroshima."
He also said there was no Japanese effort to seek a U.S. apology, "nor is there any interest in reopening the question of blame for the sequence of events that culminated in the use of the atomic bomb."
Japanese Foreign Minister Fumio Kishida, who presides over the two-day meeting, on Sunday said ministers will discuss anti-terrorism steps, maritime security and issues related to North Korea, Ukraine and the Middle East.
Some of the topics discussed on Sunday included countering violent extremism, the battle against Islamic State militants and the effort to end the five-year Syrian civil war, a second U.S. official told reporters.
Maritime security is on the cards after China rattled nerves in the region with its controversial reclamation work in the South China Sea. Some talk of nuclear nonproliferation is inevitable given North Korea's fourth nuclear test in January.
During World War II, a U.S. warplane dropped a nuclear bomb on Hiroshima on Aug. 6, 1945, reducing the city to ashes and killing 140,000 people by the end of that year.
Hiroshima's suffering is vividly displayed at the museum the ministers will tour, including their charred and torn clothes, a tricycle ridden by a three-year old boy who died from the blast and statues of the victims, their flesh melting from their arms.
Three days after dropping the atomic bomb on Hiroshima, the United States dropped one on Nagasaki. Japan surrendered six days later.