Barack Obama has been warned against intervening in the EU debate by MPs campaigning for Brexit, ahead of his visit to the UK next month.
In an open letter the group said it would be an "unfortunate milestone" for the US president at the end of his time in office to enter the debate.
Mr Obama has previously said the UK must stay in the EU to continue to have influence on the world stage.
His UK visit is likely to be his last before his term in office ends.
The UK will vote on whether to remain in the EU or leave on 23 June.
The letter from the cross-party group comes after London Mayor Boris Johnson, one of the most prominent MPs campaigning for the UK to leave the EU, said Mr Obama's suggestion the UK would be weaker on the world stage outside the EU was "wholly fallacious".
The letter's signatories said any intervention risked being undemocratic.
The letter said: "While it is understandable that a sitting US president feels the obligation to speak in the interest of the United States, it must be advised that even a passive diplomatic recommendation in the matter of our national decision will receive the opposite of the intended effect."
The group said the referendum would be a "vote of profound consequence" and it was "imperative that the question of exiting the European Union is not one answered by foreign politicians or outside interests, but rather by the British people".
They added that the UK could "thrive" outside the EU by being free to operate without tariffs and trade restrictions while having sovereignty over its affairs and control over its borders.
One of the letter's signatories, Labour backbencher Kate Hoey, said the letter aimed to caution Mr Obama that "feelings will run high" if he expressed a side in the debate.
She said: "We have chosen to respectfully request he recognises matters of sovereignty are best left to the citizens directly affected.
"We would certainly never think of visiting the United States and telling the US public how to vote in an election or the amendment of their constitution."
'Worth listening to'
Downing Street previously said Mr Obama and other leaders were "worth listening to".
A White House spokesman said it would continue to argue it "deeply values a strong ally in the United Kingdom as part of the European Union".
Mr Obama will visit the UK as part of a tour including Saudi Arabia and Germany and is expected to arrive after the Queen's birthday on 21 April.
His term in office ends in January.
Signatories of the letter, which has been sent to the White House and circulated around Washington, include UKIP's Nigel Farage, Labour MP Kelvin Hopkins, Conservatives Tom Pursglove and Peter Bone, and the DUP's Sammy Wilson.