David Cameron is travelling to Washington for his first official visit to the United States since becoming Prime Minister in May.
Strategy for what he calls a "vital year" in Afghanistan is likely to top the agenda when he meets President Barack Obama for talks at the White House on Tuesday.
But he is also expected to confront criticism of oil giant BP over both the Gulf of Mexico spill and claims by US politicians it lobbied for the release of the Lockerbie bomber to secure a deal.
Mr Cameron will conclude the two-day visit in New York with talks with UN Secretary General Ban Ki-Moon and a major trade push in meetings with senior business figures.
The PM and Mr Obama last met at the G8 and G20 summits in Canada last month, and Downing Street said Mr Cameron was keen to build on "excellent discussions" they enjoyed there.
In an interview last week, he said he believed in the special relationship between the two countries but acknowledged that Britain was its "junior partner".
"I think it is an important and long-standing relationship and I hope that we bring things to that relationship," he told Time Magazine.
The two leaders will discuss Afghanistan as ministers gather in Kabul for a major conference which is expected to endorse a 2014 target for the full transfer of security to the Afghan forces.
Four British servicemen were killed in a 24-hour period over the weekend and Mr Cameron said he wants British combat troops home by 2015.