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US President Barack Obama has called his country's relationship with the UK "truly special", following a meeting with Prime Minister David Cameron.

The president said the world was "more secure and more prosperous" when the UK and US worked together.

During their three-hour meeting, the leaders discussed Afghanistan, the Middle East, the Gulf of Mexico oil spill and the economy.

Mr Cameron called the countries' relationship "essential".

On his first official US visit as prime minister, he added that he was "confident" that reforms to the banking system would be successful.

Speaking at a press conference, Mr Cameron called the BP oil spill in the Gulf of Mexico a "catastrophe" and said it was in the interests of both countries that the company is successful.

Moving on to the release by the Scottish government of the Lockerbie bomber last year, Mr Cameron said it had been "wrong", adding: "He showed his victims no compassion... they were not allowed to die in their beds surrounded by family... neither should he."

And both leaders urged Iran to negotiate over calls to end its nuclear weapons programme.

During the talks, Mr Cameron invited Mr Obama to the UK for a state visit.

No date has been set for the trip which is not expected to happen until next year or 2012, officials travelling with the prime minister said.

The prime minister has also agreed to meet four US senators to discuss their concerns over the release of the Lockerbie bomber last year.

Mr Cameron held talks earlier with Vice-President Joe Biden, where there was "common ground on the full range of foreign policy issues," according to a Downing Street spokesman.

Talks are planned between Mr Cameron and defeated Republican presidential candidate Senator John McCain and senior figures in the US Congress.

A briefing on Afghanistan at the Pentagon is expected on Wednesday, and the prime minister is also due to meet UN Secretary General Ban Ki-moon in New York.

Four US senators are calling for an investigation into allegations that oil firm BP lobbied for the early freeing of Abdelbaset al-Megrahi, who was convicted of the 1988 bombing of Pan Am Flight 103 which killed 270 people.

The Libyan, who has terminal prostate cancer, was released by Scottish Justice Minister Kenny MacAskill in August last year on compassionate grounds.

Megrahi was said to have as little as three months to live.

BP has admitted urging the British government in 2007 to agree a wider prisoner transfer agreement with Libya, but denies any part in the decision of the Scottish government to free him.

Mr Cameron's aides said he would meet the senators, having earlier declined to do so.

But Mr MacAskill told the ´óÏó´«Ã½: "I stand by the decision I made. I reflected and followed the rules and laws of Scotland. I upheld the values and the beliefs that we seek to live by as the people of Scotland."