Obama's plea for the UK to stay in the EU came he arrived in Britain to celebrate the Queen's 90th birthday.
With the result of June's referendum looking too close to call, Obama eschewed careful diplomatic language to make a direct appeal to voters to back the Remain campaign.
"As citizens of the United Kingdom take stock of their relationship with the EU, you should be proud that the EU has helped spread British values and practices - democracy, the rule of law, open markets - across the continent and to its periphery," he wrote in an article in the Daily Telegraph.
Earlier, Canada's trade minister Chrystia Freeland said that she had "great faith and confidence" that the British would "make the right choice" in the referendum.
Freeland said Canada enjoys a "strong relationship" with both the UK and EU and refused to be drawn on suggestions that the trade agreement Canada recently concluded with the EU could be model of cooperation for a EU-UK free trade agreement in the event of a Brexit.
Speaking during a visit to Brussels on Thursday, Freeland, whose father and husband are both British, said the British has the "sovereign right" to decide its own future.
But it was the comments by Obama that were signalled out for criticism by Jayne Adye, Campaign Director of leading cross-party, grassroots Eurosceptic group Get Britain Out.
On Friday, she told this website, "President Obama's arrogance in coming to the UK to preach to Britons to vote to remain in the EU is nothing short of unbelievable. No doubt he will continue to peddle David Cameron's and the BSE campaign's myths and lies about our EU membership."
She added, "The US only wants the UK in the EU as a spy in the corporatist club called the EU. The reality is EU membership is a very bad deal for Britain in terms of democratic accountability, economic prosperity and security. Sacrificing our rights of self-government to be America's patsy is totally unacceptable.
The London-based Adye said, "It is clear the UK has had a special relationship with the US for a long time. Our trade as a proportion with the US is increasing compared to our trade with the EU which is declining.
"Unfortunately, Obama is taking this for granted in his twilight months in office, solely in pursuit of his own political legacy. He is trampling all over of our historic bonds because of his own personal contempt for our country, inaccurately conflating 21st century Britain with the British Empire.
“The Obama of 2008 - who inspired the world and spoke of hope - would have supported Brexit. Unfortunately, today's Obama is afraid of making decisions, backtracks on his promises and no longer speaks of hope. This Obama speaks only in favour of preserving the status quo, bowing to our Prime
Minister's pleas to support EU membership in return for support of the transatlantic trade and investment partnership (TTIP)."
She added, "We the 'Brexiteers' are the new champions of hope. We are the ones providing the positive alternative in contrast to 'project fear'. Despite the establishment's stitch-up, we will be voting to get Britain out on 23 June and will look forward to a successful future for the UK."