Barack Obama has told David Cameron that the UK must "fix" its relationship with Europe because it is important to the country's place in the world.
Speaking at a joint news conference, Mr Obama said ultimately if there was a referendum over membership of the European Union then the "people of the UK have to make decisions for themselves".
He said: "You probably want to see if you can fix what's broken in a very important relationship before you break it off. Seems to make sense to me."
His comments backed Mr Cameron's own position on the EU. The Prime Minister plans to renegotiate the deal the UK has with Europe and said there would not be any in-out referendum until 2017.
Mr Obama had voiced his concerns over Britain's place in Europe to Mr Cameron during a telephone conversation in January when he told the Prime Minister that "the United States values a strong UK in a strong European Union".
The leaders met to discuss a wide range of topics, including Afghanistan, the economy and Syria, and, apparently, cricket and basketball.
The two men agreed that action must be taken to end the bloodshed in Syria and push for a viable opposition government to take over in the country.
Mr Cameron said there was an "urgent window of opportunity" to act in the war-torn country, where 80,000 have been killed and five million displaced, before the "worst happens".
He said: "Syria's history is being written in the blood of her people and it's happening on our watch."
Mr Cameron said the UK would make an extra £10m available to Syrian rebels for non-lethal military aid and £30m more for humanitarian assistance.
He said: "We will double non-lethal support to the Syrian opposition in the coming year. Armoured vehicles, body armour and power generators are about to be shipped."
Mr Obama said the US would be "very persistent" in pursuing a peaceful political transition that leads to Bashar al Assad's exit but leaves Syria "intact".
He said: "I'm not promising it is going to be successful. Frankly, sometimes once the furies have been unleashed in a situation like we are seeing in Syria, it's very hard to put things back together."
The Prime Minister said that he and Mr Obama had also agreed to "tackle the scourge of tax evasion" by multinational companies.
Mr Cameron also used the meeting to launch negotiations on an EU-US free trade deal ahead of next month's G8 summit in Northern Ireland.
Mr Cameron believes such a deal would boost the British economy by £10bn and the US economy by £63bn annually.
Mr Cameron's visit to Washington comes ahead of a potentially divisive vote in the House of Commons on Wednesday over whether the Government's agenda for this year should include a bill to pave the way for a referendum on membership of the EU.
Education Secretary Michael Gove and Defence Secretary Philip Hammond said they would vote in favour of Britain leaving the EU if there was a vote today.
The Prime Minister has moved on to the US from Russia. He told reporters on his way to the US that he had been "heartened" by his talks with Russian president Vladimir Putin about Syria.
Russian support for the Assad regime has been one of the main obstacles to easing the situation, but the West has appeared split on whether to respond by arming rebels.
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