 "Obama says Cameron should fix relationship with EU")
Speaking at a joint White House news conference, Obama delighted Cameron's advisers by endorsing his EU strategy at a time when the British leader is facing a revolt within his ruling Conservative party over the issue that threatens his re-election hopes in 2015.
Cameron is keen to unite his party on Europe, an issue that helped bring down Conservative prime minister Margaret Thatcher and dogged her successor John Major, another Conservative.
In his strongest statement on the subject yet, Obama said he agreed with Cameron's assessment that the EU was flawed and needed fixing, backing the prime minister's plan to try to overhaul the 27-nation bloc before giving Britons a vote on whether they want to stay or leave it.
"I will say this, that David's basic point that you probably want to see if you can fix what's broken in a very important relationship before you break it off makes some sense to me," said Obama.
"I, at least, would be interested in seeing whether or not those (reforms) are successful before rendering a final judgment."
Obama's foray into a fractious British debate gives Cameron a boost at a time when his leadership is under growing pressure from a powerful wing of his own party and a surging anti-EU party.
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Superstate
Eurosceptics in Cameron's Conservative Party see the European Union as an oppressive, interfering and wasteful "superstate" that threatens Britain's sovereignty and puts an excessive regulatory burden on its companies.
Cameron agrees, but wants to change it from within.
At a time when the euro currency zone is eyeing deeper integration, he says it is right that Britain reviews its membership as it originally only signed up to a free trade zone.
However, the prospect of a British withdrawal from Europe after 40 years has rattled many business leaders. They fear that pulling away from Britain's biggest trading partner will badly damage its fragile economy.
Faced with the prospect of many of his own Conservative lawmakers voting to censure his government for failing to enact legislation to prepare for a referendum, Cameron's position was beginning to fray as two of his own ministers expressed more sceptical views than his own.
Cameron's room for manoeuvre is limited because his pro-EU junior coalition partners, the Liberal Democrats, oppose a referendum.
But the growing popularity of the anti-EU UK Independence Party (UKIP), which did well in local elections by appealing to traditional Conservative voters, has unnerved some in his party who fear it will split the centre-right vote in 2015.
Though timely, Obama's support of Cameron's stance was nuanced.
Close ally
Ultimately, he made it clear he thought that Britain's interests and those of the United States were best served by his close ally remaining inside the EU.
"We believe that our capacity to partner with a United Kingdom that is active, robust, outward-looking, and engaged with the world is hugely important to our own interests, as well as the world," said Obama. "I think the UK's participation in the EU is an expression of its influence and its role in the world."
Officials in several European countries have warned Cameron he cannot have an "a la carte Europe", choosing the bits he likes while discarding other parts he doesn't. Several high-profile critics at home have also said Cameron has no chance of reworking Britain's EU membership.
Earlier on Monday, Cameron had tried to quell talk of a revolt in his party, saying all his ministers backed his EU strategy.
Despite a growing clamour in his party to harden his line on Europe, Cameron stuck to his pledge to try to reform Britain's EU role, saying it would be wrong to give up before renegotiation talks have begun.
"You shouldn't give up before a negotiation has started," Cameron said. "The idea of throwing in the towel before the negotiations have started is a very, very strange opinion."
Up to 100 eurosceptic Conservative members of parliament are expected to back an amendment this week criticising legislative plans unveiled by the government because they did not include a bill paving the way for a referendum on Britain's EU membership.
UKIP leader Nigel Farage said the only way Cameron could solve his Europe problem was to hold a referendum before the next election.
"If he doesn't, then I think he will go on leading a party that is hopelessly split," Farage told the BBC. "The dam has broken. I think the politics that dare not speak its name has now become mainstream."