UPDATED 2:23 p.m. ET
(CBS News) -- President Obama on Wednesday said the United States is continuing to make progress in Afghanistan and would keep its existing plan for that nation to control its own security less than three years from now.
"I am confident we can put Afghans in a position where they can deal with their own security," Mr. Obama told reporters at the White House after meeting with British Prime Minister David Cameron.
International forces are scheduled to take on a supporting role in 2013 and the Afghan forces are expected to be responsible for their own security by the end of 2014.
"I don't anticipate at this stage that we are going to be making any sudden additional changes to the plan that we currently have," he said in a joint press conference with Cameron at his side.
The comments come just days after a shooting in Afghanistan, where a U.S. solider has been accused of killing 16 civilians, many of whom were asleep. The alleged shooter was flown out of Afghanistan to a detention facility in another, undisclosed, nation. Afghan President Hamid Karzai knew about, and approved of, the decision to move the alleged gunman, a U.S. official told CBS News Pentagon correspondent David Martin.
"What's undeniable, though, and what we can never forget is that our forces are making very real progress dismantling Al Qaida, breaking the Taliban's momentum, and training Afghan forces so that they can take the lead and our troops can come home," Mr. Obama said.
Cameron, for his part, echoed the message.
"But I think what we're trying to do by the end of 2014 is achievable and doable," Cameron said, "what's happening in Afghanistan today is quite different to the situation we had three, four, five years ago."
The United States is expected to reduce its troop force to about 68,000 by the end of September from about 91,000 in Afghanistan now.
The attack comes on the heels of another incident that caused increased hostility toward the U.S. presence in Afghanistan -- the burning of Muslim holy books last month. That incident led to a week of riots and attacks that left 30 people dead, including six U.S. soldiers.
Just hours before the two men walked into the Rose Garden to take questions from reporters, Defense Secretary Leon Panetta's plane was diverted after an Afghan driver somehow caught fire after crashing a stolen truck at roughly the same time andat a British base in Afghanistan. U.S. officials said Panetta was not in danger.
Asked why many Americans and Britons are skeptical of the progress that the two leaders frequently tout, Mr. Obama said polls show that people want to end the war because it has been going on for a decade.
"People get weary, and they know friends and neighbors who have lost loved ones as a consequence of war. No one wants war," Mr. Obama said.
Cameron is in the United States for a three-day official visit and is to attend a state dinner at the White House on Wednesday night.