President Barack Obama gave his fullest endorsement yet for the mission shift, but he said the overall plan to gradually withdraw forces and hand over security in Afghanistan will stand.
Obama said he anticipates no "sudden, immediate changes to the plan we already have," for bringing forces home.
The United States and Britain have the largest fighting forces in Afghanistan, where the combat is in its 11th year. The U.S., Britain and other NATO nations have already agreed to keep forces in the country through 2014, when Afghan President Hamid Karzai will leave office.
"At the upcoming NATO summit in my hometown of Chicago, we'll determine the next phase of transition," Obama said following a private meeting at the White House with visiting British Prime Minister David Cameron. "This includes shifting to a support role next year in 2013 in advance of Afghans taking full responsibility for security in 2014. We're going to complete this mission and we're going to do it responsibly."
Obama acknowledged the drop in public support at home for the war. "People get weary," after long wars, the president said, but he also said he thinks most people in both the U.S. and Britain understand the reasons for continuing the fight.
Cameron, who joined Obama for a joint Rose Garden news conference, said security is better in Afghanistan and he praised the U.S. strategy to add more than 30,000 forces in a "surge" against the Taliban-led militants in 2009.
"The situation is considerably improved," Cameron said, and the goal of keeping Afghanistan from again becoming a terrorist haven is achievable by the end of 2014.
Following the summer fighting season, Obama said NATO allies would look at how to continue drawing down forces at a gradual pace.
The Obama-Cameron meeting came in advance of May's NATO summit in Chicago, where a decision on the timetable for withdrawal from Afghanistan is expected to be confirmed.
The White House discussions follow the weekend killings of 16 Afghan civilians, allegedly by a lone U.S. soldier, and the deaths of six British troops last week in a roadside bomb blast - the largest loss of life in a single incident for British forces in Afghanistan since 2006.
On Iran, Obama insisted there is still "time and space" for a diplomatic solution, in lieu of a military strike to set back Iran's progress toward a possible bomb, but said "the window for diplomacy is shrinking."
"We are determined to prevent Iran from acquiring a nuclear weapon," Obama said, adding that he had sent a message "personally" to the Iranian leadership that it should re-enter international arms talks in good faith.
"Tehran must understand that it cannot escape or evade the choice before it. Meet your international obligations or face the consequences."
The White House lavished Cameron with all the pomp and pageantry of a state visit as the two allies aimed stressed their unity in dealing with hot spots like Iran, Syria and Afghanistan. At a welcoming ceremony, military bands and a large crowd were arrayed before Obama and Cameron, with Vice President Joe Biden and top administration officials including Secretary of State Hillary Rodham Clinton standing for a 19-gun salute and the national anthems of both nations.
Amid concerns in Britain that U.S. focus is drifting toward East Asia, Obama sought to reassure the British leader with a fancy White House dinner and a warm and personal show of support.
Despite the rapid rise of China and other emerging economic powers, Cameron said the U.S. and Britain remain one another's most significant international partners.
"Yes, the world is changing at a faster rate than ever before," he said. "But one thing remains unchanged: the ceaseless back and forth between our two nations of ideas, friendship, business and shared endeavor."
The serious talks follow a more relaxed day in which Obama and Cameron flew to Dayton, Ohio, to watch an NCAA tournament college basketball game between Mississippi Valley State and Western Kentucky - a new experience for the British leader. Obama gave Cameron the royal treatment, inviting him to fly on Air Force One and enjoy a quintessential American tradition.
Cameron and Obama also will consider how to increase pressure on Syrian President Bashar Assad, amid the yearlong uprising during which the U.N. estimates his regime has killed over 7,500 people. Britain's ambassador to the U.S., Peter Westmacott, said Obama and Cameron had a strong shared conclusion that military action is not the way to solve the crisis.
During his visit, Cameron also is expected to meet with New York Mayor Michael Bloomberg and Newark, N.J., Mayor Cory Booker - but he won't hold talks with any of the Republican presidential candidates.