* Cameron seeks to quash perception of disagreement with US
* Says US backs UK bid to stay in EU but change relationship
By Andrew Osborn
LONDON, Jan 11 (Reuters) - Britain on Friday sought to counter perceptions of discord with the United States over the European Union, saying U.S. President Barack Obama had told Prime Minister David Cameron that he supported his drive to renegotiate Britain's EU membership.
Relations between the two close allies came under the spotlight earlier this week after a senior U.S. official made a rare and forceful foray into what is an emotive domestic debate, saying Washington wanted Britain to stay in the EU - a position not shared by a majority of the British public as well as hardliners in Cameron's own ruling Conservative party.
But Cameron's spokesman said on Friday that the two governments saw eye to eye on the issue and that Obama and the prime minister had discussed the subject in a phone call the week before Christmas.
"The prime minister took the president through our approach to the EU and the president was supportive of it," the spokesman told reporters in London.
"He (Obama) is supportive of the prime minister's view that Britain's national interest is to be within the EU but to change the relationship with the EU."
Cameron is expected to deliver a major speech later this month in which he will set out which powers he wants Britain to repatriate from the 27-member EU, along with the terms of a historic vote on the subject that could help define Britain's role in international affairs for decades.
The intervention by Philip H. Gordon, the U.S. assistant secretary of state for European and Eurasian affairs, was the first time a U.S. official had made such comments in public.
It created the impression that Washington was anxious about Cameron's plan to reshape Britain's EU ties and provoked a furious response from hardliners inside the ruling Conservative party who felt the United States was interfering in a domestic matter.
But both countries have since been keen to play down the significance of Gordon's comments.
In Washington, State Department spokeswoman Victoria Nuland stressed on Thursday that any decision on EU ties was for the British government and people to make, saying Gordon's comments merely restated what she said was a well-known U.S. position on the subject.
"We generally don't have assistant secretaries of state going out and giving press conferences and freelancing," Nuland said. "Assistant Secretary Gordon very much spoke for the administration."
In London, the prime minister's spokesman has also played down any idea of a rift, saying Cameron agreed with Gordon in so far as he also wanted to see "an outward-looking EU with Britain in it".
Cameron faces a dilemma. Many MPs in his own Conservative Party are pressuring him to call a full-fledged referendum on whether Britain should remain in the EU - a demand backed by opinion polls which show a majority of Britons would, if given the chance, vote to leave the bloc.
But business leaders in Britain have said they are strongly opposed to the prospect of the country radically downgrading ties with its biggest trading partner.
International partners from the United States to Germany and Ireland have made it clear they oppose a British EU exit - "Brixit" - and believe that such a move would isolate and damage Britain itself.