David Cameron should apologise for his description of Donald Trump as "divisive, stupid and wrong", according to an adviser to the US presidential hopeful.
George Papadopoulos said it would be "wise" for the Prime Minister to "reach out in a more positive manner" to the Republican front-runner.
Mr Cameron was trenchant in his criticism of Mr Trump last December, when Parliament debated a petition to ban him from the UK over his call for a "total and complete shutdown of Muslims entering the United States".
The PM told the House of Commons he opposed a travel ban on Mr Trump, but added: "I think his remarks are divisive, stupid and wrong. If he came to visit our country I think he would unite us all against him."
Mr Papadopoulos, an adviser to the property tycoon and reality TV star, told The Times: "First we need an invitation. Of course if the United Kingdom extended an invitation it would be a tremendous show of unity and a wonderful spectacle.
"That invitation has not yet been extended ... but if it is it would be received in a positive way."
Asked if Mr Trump would forgive Mr Cameron's comments, Mr Papadopoulos told the newspaper: "I can't speak directly for him but it would seem that if Prime Minister Cameron is serious about reaching out, not only to Mr Trump's advisers but to the man himself, an apology or some sort of retraction should happen.
"To see Mr Cameron come out as the most vocal opponent was uncalled for. Considering that we believe that the UK-US relationship should be a cornerstone, not just of Nato policy but elsewhere, it would be wise for him to reach out in a more positive manner to Mr Trump."
Mr Cameron was asked to comment on Mr Trump's White House bid by US reporters travelling with President Barack Obama on his two-day visit to the UK.
The PM said he would neither add nor subtract from his earlier remarks about Mr Trump, who looks set to become the Republican candidate to take on Hillary Clinton in this year's election.
Speaking alongside Mr Obama at a press conference, Mr Cameron said: "As for the American elections, I have made some comments in recent weeks and months. I don't think now is the moment to add to them or subtract from them.
"But I think, as a prime minister who has been through two general elections leading my party, you always look on at American elections in awe at the scale of the process and the length of the process and I marvel at anyone who's left standing at the end of it."
Downing Street has previously confirmed that Britain's ambassador in the US has been "engaging" with Mr Trump's team as "part and parcel" of the UK's usual efforts to establish good links with presidential candidates.
Prime ministers are traditionally wary of making any public comment about candidates in elections overseas, for fear that they may be accused of attempting to interfere in the democratic decisions of foreign nations, or that their words may come back to bite them if they later have to deal with the candidate in office.
At the time of Mr Cameron's criticism, Mr Trump was widely regarded as a maverick candidate who would struggle to translate his popular appeal into a Republican nomination or a credible bid for the White House.