Reuters
BBC North America editor John Sopel said the president had not needed to make his intervention and could have been much more nuanced.
"That he has is a mark of the profound concern felt in Washington about the implications of a British departure from the EU," he said.
However, BBC political editor Laura Kuenssberg said a Brexit-supporting cabinet minister had stressed that Obama's view "was not the settled view in the USA. The Republicans don't agree and there is disquiet at his blatant meddling in UK politics".
The minister had suggested Ted Cruz supported Brexit, she added.
'Stick together'
Speaking to the paper, Mr Obama said that the US's relationship with the UK had been "forged as we spilt blood together on the battlefield".
He went on to say the UK had benefitted from being inside the EU in terms of jobs, trade and financial growth, and that it "magnifies" the UK's global influence.
"This kind of co-operation - from intelligence sharing and counter-terrorism to forging agreements to create jobs and economic growth - will be far more effective if it extends across Europe. Now is a time for friends and allies to stick together," he wrote.
Reuters
Former US State Department spokesman James Rubin told BBC Breakfast the president had not offered any words of reassurance about Britain's future relationship with the US if it left the EU because "it won't be OK".
"We have a phrase in America: 'Friends don't let friends drive drunk,'" he said, adding that it would be "a big mistake for Britain to leave the EU and set asunder what has been a very successful relationship".
'Perverse'
But Vote Leave's Boris Johnson said although he was a "big fan" of Mr Obama, remaining in the EU is "clearly something we have a disagreement on".
He said: "It's perverse that we're being urged by the United States to embroil ourselves ever so deeply in a system where our laws, 60% of them, are now emanating from the EU.
"America's a proud democracy built on principles of liberty. It is hypocritical for us to be told by America to embroil ourselves ever more deeply in a structure which would be absolutely alien to American traditions.
"I think most Americans would accept that there is something rum about asking us to subordinate our democracy in this way, when America would not dream in a million years of doing likewise".
AP
Mr Johnson originally criticised Mr Obama in an article in the Sun but has since been criticised for making comments about the president's "part-Kenyan" ancestry.
He pointed to claims Mr Obama had an "ancestral dislike of the British Empire" because of his own heritage.
Labour's Diane Abbott branded the comments "offensive" and Lib Dem Lord Campbell said they were "unacceptable".
Tory MP Iain Duncan Smith, who is also part of the Vote Leave campaign, accused Mr Obama of double standards.
"I can imagine no circumstances under which he would lobby for the US Supreme Court to be bound by the judgements of a foreign court," he said.
"Nor can I imagine any circumstances in which he would accept that laws should be made for - or taxes imposed on - the people of the United States without the approval of Congress."
Mr Obama's UK stay is part of a tour taking in Germany and Saudi Arabia, which he left on Thursday after having discussions with King Salman on issues including Iran, Syria, Yemen and the fight against so-called Islamic State militants.
