The Foreign Secretary has clashed with Boris Johnson over his claim it would be "hypocrisy" for Barack Obama to intervene in the EU referendum debate.
Philip Hammond defended the right of foreign leaders, including the US president, to speak up about their hopes for the UK to continue to be a member of the European Union.
He suggested that voters could be "deceived" by claims from some in the Brexit camp about the possibility of strengthened relations with English-speaking countries in the event of a vote to leave the EU.
Downing Street has refused to comment on reports that the US president, who has previously made it clear that America wants its closest ally to remain part of the EU, is heading to the UK next month to make the case to voters.
Speaking at a meeting of EU foreign ministers in Brussels, Mr Hammond said that although the referendum is a matter for the British people to decide, "it is those who are campaigning for an Out vote who have talked so much about the Anglosphere, about Britain's alternative possibilities if we were to exit".
He added: "I think it's important that we hear from those people in the Anglosphere - not just President Obama but the leaders of Australia, New Zealand, Canada - and beyond the Anglosphere, Japanese and Chinese leaders. Let's just hear what they actually think about their relations with Britain.
"Let's just hear how much they actually value Britain's membership of the EU, just so the British people are properly informed in this debate and are not deceived by some of the suggestions they are hearing about the welcome that might be awaiting us if we left the EU from our English-speaking partners around the world."
Mr Johnson defended his stance, telling the Press Association it was a "paradox" for the United States to call for the UK to remain in the EU.
He said: "The traditional American position on this, which is what I expect the president will develop, is that Britain should stay in, should integrate further within the European Union because America conceives it as very much being in Washington's interests for us to be there, to be their eyes and ears, to be batting for them on some of these issues such as cyber security or indeed the development of the internet and all the rest of it.
"That's great and I think it is a very important argument. However I think that the UK's influence in these things can be expressed in lots of other ways, lots of other forums, and within the EU it is steadily being diminished.
"I just call attention to the paradox that we should be urged down this path towards the creation of a federal European Union by a country that absolutely zealously guards its own sovereignty and refuses to share powers with anybody at all.
"The United States, virtually alone of Western nations, and not just Western nations, virtually alone in the world, refuses to allow its citizens to be subject to the international criminal court, it hasn't signed up to the convention on the law of the sea. It is a paradox, to put it mildly, that we should be urged by the United States to do this."
Speaking on a visit to the Olympic Park in east London, Mr Johnson added: "We are the fifth biggest economy and the point we are making in the Vote Leave campaign is that this is our chance to strike free trade deals around the world and go forward with a different approach, better for Britain, better for Europe."
Asked if he would meet Mr Obama to put his views across if the president visits the UK, he said: "I have no idea, I think at the present rate of fire I think it unlikely, but you never know."
Downing Street refused to be drawn on whether David Cameron would welcome a further intervention by the US president.
The Prime Minister's official spokeswoman said: "The PM is focused on getting out and about around the country making the case for why we think it's in the UK's interest to stay in a reformed EU.
"He said when he was in France at the summit recently that lots of people are making their views known on this issue, including international leaders. These are people who wish Britain well and they are worth listening to.
"But because the Prime Minister is the one that has delivered on his promise of a referendum, it will be up to every person in this country to make up their own mind about whether Britain should remain or leave."
She added: "Other people will set out their views. The choice for the British people is whether or not they listen to them, but then they get to make up their own minds."
The spokeswoman declined to confirm or deny reports that Mr Obama may be paying a visit to the UK in April.
In his regular Daily Telegraph column, Mr Johnson wrote that it would be "a piece of outrageous and exorbitant hypocrisy" for the leader of the United States to express support for the UK remaining in the EU.