US President Barack Obama met Prime Minister David Cameron on Friday after appealing to British voters to stay in the European Union, telling them the United States "needs your influence to continue."

Obama met Cameron in London following a private lunch at Windsor Castle with Queen Elizabeth II, who turned 90 on Thursday, and her husband, Prince Philip.

Obama and his wife, Michelle, gave the queen a photo album "chronicling her visits with US presidents and first ladies" and highlighting "the enduring close friendship" between the United States and Britain as a birthday gift, the White House said.

Obama's talk with Cameron was expected to cover Libya, Syria, the fight against Islamic State and other international issues.

But Obama's arrival in London was overshadowed by a row over his intervention on Britain's June 23 referendum on whether to remain in or leave the EU.

Cameron, who is leading efforts for the country to remain in the bloc, backed Obama's right to give his views.

"The US is one of our closest allies," Cameron wrote on Twitter. "So it's important to hear Barack Obama on why we should remain in the EU."

Writing in The Telegraph, Obama said Britain's security and economic growth would be better if it remained part of the EU.

"The United States sees how your powerful voice in Europe ensures that Europe takes a strong stance in the world, and keeps the EU open, outward looking, and closely linked to its allies on the other side of the Atlantic," he said.

"So the US and the world need your outsized influence to continue - including within Europe," Obama said.

Campaigners for a Brexit, or British exit from the EU, criticized his intervention. Iain Duncan Smith, a leading eurosceptic in Cameron's Conservative Party, accused the US president of trying to "intimidate the British people into voting to stay in the EU."

Writing in The Sun, London Mayor Boris Johnson, another Conservative backer of Vote Leave, called Obama's appeal to Britain "a breathtaking example of the principle of 'do as I say, but not as I do.'"

Critics slammed Johnson after he claimed the White House could have removed a bust of British wartime prime minister Winston Churchill because of the "part-Kenyan" president's "ancestral dislike of the British empire."

Cameron and Obama are scheduled to hold a joint press conference at Downing Street, the prime minister's official residence in London, following their talks.

They are expected to reaffirm the "special relationship" between the two nations after the White House said ahead of Obama's visit that the United States has "no closer friend in the world" than Britain.

Obama is scheduled to attend a dinner with other members of the royal family Friday, and on Saturday he will host a "town hall" question-and-answer event in London and attend a dinner with Cameron.

In The Telegraph, he stressed the EU's role in pursuing a nuclear deal with Iran and the Paris climate agreement, and he also addressed the key economic debate for and against Brexit.

"When it comes to creating jobs, trade, and economic growth in line with our values, the UK has benefited from its membership in the EU," he wrote.

He said that in the end, however, the vote was "a matter for British voters to decide" for themselves.

The controversy over Obama's reiteration of his opposition to a Brexit had begun before his arrival.

An open letter from UK Independence Party leader Nigel Farage and other founders of the Leave movement asked Obama to "abstain from any intended advocacy" on the referendum, while an online petition to parliament, signed by some 35,000 people, called for him to be gagged.

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