William Hague will hold talks in Washington today on his first overseas visit after being appointed Foreign Secretary in the new coalition government.
The conflict in Afghanistan is likely to top the agenda for his discussions with United States secretary of state Hillary Clinton.
Mr Hague has promised to pursue a "solid but not slavish relationship" with America, while recognising the "huge importance" of the so-called special relationship.
He arrives hot on the heels of a four-day visit by Afghan president Hamid Karzai - who he has said would be urged by the new power-sharing administration to meet his commitments.
The Government "will give time and support for the strategy to succeed" but "that does involve the government of president Karzai implementing any commitments that it has made.
"He has been in Washington all week, president Karzai, working with the US government on their strategic partnership for the future, on implementing the commitments made, so of course we are hoping he will do that," the Foreign Secretary told the BBC.
He said British troops would remain in Afghanistan until "their job is done" and refused to set any "artificial deadline" for the withdrawal of armed forces from the conflict zone.
"We will take stock together, but we are not looking here at setting artificial deadlines, arbitrary deadlines, a date of withdrawal," he said.
There were no "sharp differences" between the approaches of the Conservatives and their Liberal Democrat coalition partners on the conflict, he insisted.
US President Barack Obama was the first world leader to telephone David Cameron to congratulate him on becoming Prime Minister.
His country had "no closer friend and ally than the United Kingdom", Mr Obama told him and extended an invitation to the White House in July.
Asked about the special relationship as he took up his new role, Mr Hague said: "No doubt we will not agree on everything,
"But they remain, in intelligence matters, in nuclear matters, in international diplomacy, in what we are doing in Afghanistan, the indispensable partner of this country.
"So that approach will be very much alive under this coalition Government."
General Sir Richard Dannatt, the former head of the Army, said he thought David Cameron and Nick Clegg understood that Afghanistan "is a really important issue".
He told BBC Radio 4's Today programme: "It was no surprise I think that William Hague has gone to the United States this morning and top of the agenda is Afghanistan.
"It is absolutely right that our government, the US government talks about these things and we are all absolutely clear that a) this is important, b) it's got to be done well and let's get on with it as quickly as we can."
From the Foreign Office: Pictures of the incoming Foreign Secretary