Writing in the Wall Street Journal on Tuesday, Cameron said Britain was clearly junior to its "oldest and staunchest ally" but should behave in a way that reflected a nation clear in its views and values.
"The US-UK relationship is simple: It's strong because it delivers for both of us," he wrote.
Relations between the two countries have been complicated in recent weeks by growing US anger towards British-based energy giant BP over its handling of the Gulf of Mexico spill.
The US has also raised questions over whether BP played a role in the release last year of the convicted Lockerbie bomber Abdel Basset al-Megrahi from a Scottish prison.
|US criticism of British energy giant BP could overshadow the White House talks [Reuters]
British officials have tried to play down concerns ahead of Tuesday's meeting, saying the US debate over how al-Megrahi was allowed to return home to Libya "may come up" during talks, but was not a "major issue".
BP has confirmed it lobbied the British government in 2007 over a prisoner transfer agreement with Libya, but said it was not involved in talks on al-Megrahi's release, which was strongly opposed by the Obama administration.
Cameron's office said on Tuesday it had no plans to re-examine the case, despite demands by US politicians for an investigation to determine whether the decision to free him was made to facilitate Libyan oil deals for BP.
Vincent Moss, political editor for the Sunday Mirror newspaper in London told Al Jazeera that the issue of Megrahi had been "building up unpleasantly for David Cameron over the last few days".
"It was a decision taken the Scottish government and a decision that Cameron opposed. But that will be rather lost in the American media - they think that britain was comlicit in this, endorsed it. This is going to be a big problem for Cameron in America today."
Hillary Clinton, the US secretary of state, said the United States would continue to maintain in exchanges with Scottish officials "our unshakable conviction that al-Megrahi should not be a free man".
Moss added that many in the US were holding the BP oil spill and the release of Megrahi against the UK.
Lockerbie and BP aside, Cameron has said he wants both nations to make progress on exit strategies for Afghanistan and getting the global economy back on track.
A changing global environment, in which nations such as China are challenging Western economic supremacy, has transformed British foreign policy priorities and put more emphasis on seeking business and influence in emerging markets, he has said.
Cameron will visit Turkey and India after his two-day trip to Washington and New York.
"In a world of fast-growing, emerging economies, we have a responsibility to engage more widely and bring new countries to the top table of the international community," he wrote in Tuesday's Wall Street Journal article.
"To do so is pro-American and pro-British, because it's the only way we will maintain our influence in a changing world."