Defence Secretary Liam Fox says British troops may be among the last to leave Afghanistan and "strategic patience" is required.
He told the BBC that he believed Helmand, where British troops are, was likely to be "one of the last places they will be able to transition from".
The strategy should be given "time to work... without constantly trying to change and question it," he said.
Dr Fox spoke in Washington where he held talks with his US counterparts.
He met US Defence Secretary Robert Gates, other senior administration officials and members of Congress.
In a BBC interview, Mr Fox said the bottom line was that "the likelihood is that it [Helmand] will be one of the last parts to transition over to Afghan charge".
"The mission in Helmand is one of the most difficult ones and I imagine one of the last places they will be able to transition from," he added.
"And I think with the Americans, we need to ensure that we do in the future as we have done already - which is to have a fully integrated mission as part of a genuine coalition."
In a speech in Washington, he said that it is important for people to keep their nerve about the mission.
To leave before the job was done would send a message to the enemy, he said.
"It would send the signal that we did not have the moral resolve and political fortitude to see through what we ourselves have described as a national security imperative."
US President Barack Obama is planning a full review of the strategy by the end of the year, but in his interview Dr Fox warned: "We've got to give it time to work. We can't pull a plant up every day to look at its roots to see how it is growing."
He said that leadership was all about being positive: "We've got to give the strategy time to work on the ground without constantly trying to change and question it."
His comments come days after Prime Minister David Cameron said he wanted to see troops home by the time of the next general election, due in 2015.
Mr Fox later visited the Walter Reed Army Medical Centre where he met staff and US service personnel injured in Afghanistan and Iraq.
"Our brave armed forces are paying a high price defending national security which is why both the UK and the US governments are committed to providing the best quality of care and rehabilitation to our injured service personnel," he said.