Boris Johnson has attacked the prime minister for achieving "two thirds of diddly squat" in his pre-referendum negotiations with Brussels.
The London Mayor hit back at his critics for "crowing too soon" in his Daily Telegraph column.
On his visit to the UK, Obama said being part of the European Union "enhances Britain's global leadership".
So I gather they think it's game over. The Bremainers think they have bombed us into submission.
They think that we have just seen the turning point in the referendum campaign, and that the British people are so intimidated by these testimonials - American presidents, business leaders, fat cats of every description - that they now believe the British people will file meekly to the polls in two months time and consent to stay in the EU; and thereby to the slow and insidious erosion of democracy in this country.
If that is indeed the view of the Remain campaign, they are crowing too soon.
US President Barack Obama on Sunday praised German Chancellor Angela Merkel's handling of Europe's migrant crisis saying "she is on the right side of history."
Speaking at a news conference at the opening of a trade show in Hanover, Obama praised her reaction to the millions of refugees and migrants fleeing war and poverty in the Middle East and Africa.
"In this globalised world, it is very difficult for us to simply build walls."
The President also said the free trade deal between the European Union and United States must move forward.
The Transatlantic Trade and Investment Partnership (TTIP) agreement which supporters say could boost each economy by $100 billion is still being negotiated.
Tens of thousands marched against the deal in Germany on Saturday warning it could undermine the rights of workers and consumers and weaken environmental protections.
U.S. President Barack Obama has found time during his official whirlwind visit to the UK to take time out for a spot of golf with Prime Minister David Cameron.
The two politicians played a round of golf at The Grove, just north of London today, after Obama met with Labour Party leader Jeremy Corbyn to discuss "the challenges facing post-industrial societies and the power of global corporation".
President Barack Obama will meet Labour leader Jeremy Corbyn on Saturday, the White House said.
The meeting is expected to be closed to the media.
Mr Corbyn has been an outspoken critic of President Obama's foreign policy, once referring to him as a "Pentagon president like all the others".
President Obama and the First Lady have been welcomed by the Duke of Duchess of Cambridge and Prince Harry at Kensington Palace, where they will have dinner this evening.
US President Barack Obama has arrived at Windsor Castle to have lunch with the Queen.
The Queen and Duke of Edinburgh will host a private lunch for the US President and his wife Michelle at Windsor Castle.
It is a post-birthday affair for the Queen, who turned 90 yesterday, so the Obamas are expected to come bearing a gift.
Leave campaigners "can't claim" they want a closer relationship with the US and then say that President Obama has "no right to speak" about the EU referendum, according to Labour MP Alan Johnson.
ITV News Deputy Political Editor Chris Ship tweeted:
US President Barack Obama has arrived in the UK for an official four-day visit which will see him meet the Queen for her birthday celebrations, have dinner with William and Kate, and try to persuade British voters not to leave the EU.
The President touched down aboard Air Force One at Stansted Airport shortly after 9.30pm this evening before transferring on to a private helicopter.
The Duke and Duchess will be joined by Prince Harry at the power dinner for the US president Barack Obama and his wife Michelle.Read the full story ›