David Cameron met with George Bush yesterday as he attempts to repair his party's ties with the Republicans.
The Tory leader said the meeting, which lasted a little under half an hour, was "very positive".
Mr Cameron insisted he had "got on very well" with the US president and the pair discussed Iran, Afghanistan, free trade and climate change.
He told reporters: "We had a good conversation about some issues that Britain and America really need to work together on."
It marked Mr Cameron's first trip to Washington since becoming Conservative leader, with relations between the two right-wing parties frayed since Michael Howard criticised Tony Blair for the war in Iraq.
Mr Bush did not formally meet with Mr Cameron but "dropped by" on a meeting between the Tory leader and US national security adviser Stephen Hadley.
In a bid to position himself as a prime minister-in-waiting - and one prepared to reprioritise the links between the Conservatives and the Republicans - Mr Cameron used his visit to Washington to set out his foreign policy.
In a speech to the Brookings Institute, he said he represented a new generation of "proudly Atlanticist" leadership in the Conservatives.
He said the relationship between the two nations was special and "will remain special for any British government I lead".
But Mr Cameron cautioned the special relationship, which dogged Tony Blair during his last few years in power, must remain grounded in the "ability to talk freely to each other as only old friends can".
Mr Cameron said the UK and US must "stand together against global terrorism fuelled by a perversion of the Islamic faith".
He continued: "My view is clear: the cause of peace and progress is best served by an America that is engaged in the world. And the values we hold dear are best defended when Britain and the United States, and the United States and Europe, stand together."