Boris Johnson and Jeremy Hunt have criticised Donald Trump for telling four US congresswomen to "go back" to the "broken and crime infested places from which they came" – but refused to condemn the remarks as racist.
The Tory leadership rivals both said they agreed with Theresa May's condemnation of the remarks made by the US president on Twitter as "completely unacceptable".
While Mr Trump did not name the four, he is believed to have been referring to congresswomen Alexandria Ocasio-Cortez, Ilhan Omar, Ayanna Pressley and Rashida Tlaib.
Only Ms Omar, from Somalia, is foreign-born.
Asked about the comments, at a debate hosted by The Sun, Mr Johnson said: "If you are the leader of a great multiracial, multicultural society you simply cannot use that kind of language about sending people back to where they came from.
"That went out decades and decades ago and thank heavens for that so it's totally unacceptable and I agree with the Prime Minister."
Pressed on whether the comments were racist, he said : "I simply can't understand how a leader of that country can come to say it."
Pressed again, he replied: "You can take from what I said what I think about President Trump's words."
Mr Hunt said the remarks were "totally offensive", but challenged on whether the remarks are racist, he said it would not be helpful to use such language about the US president.
Mr Hunt said: "I have three half-Chinese children, and they are British citizens born on the NHS, and if anyone ever said to them 'go back to China', I would be utterly appalled."
He added: "I think that, look I'm Foreign Secretary, this is a president of a country which happens to be our closest ally and so it is not going to help the situation to use that kind of language about the president of the United States.
"I can understand how many people in this country would want politicians like me to use those words and would feel that sentiment but I will make absolutely clear, I hope I have made absolutely clear, how totally offensive it is to me that people are still saying that kind of thing."
Earlier Scottish Tory leader Ruth Davidson said Mrs May was right in her assessment, adding "and both men vying to be her successor should say so".
Mr Trump had hit out at the congresswomen "who originally came from countries whose governments are a complete and total catastrophe, the worst, most corrupt and inept anywhere in the world" and suggested "why don't they go back and help fix the totally broken and crime infested places from which they came".
His comments led to attacks from senior Democrats, with presidential hopeful Elizabeth Warren condemning the "racist and xenophobic attack" and another 2020 contender, former Texas representative Beto O'Rourke saying "this is racist".
Despite the widespread outrage provoked by his tweets, the president seemed unfazed.
Speaking at the White House on Monday he said: "If you're not happy in the US, if you're complaining all the time, you can leave, you can leave right now."
Scotland's First Minister Nicola Sturgeon said the president's comments were "not OK and diplomatic politeness should not stop us saying so, loudly and clearly".
The latest row follows the storm created by the leak of sensitive diplomatic messages from the UK's ambassador in Washington, Sir Kim Darroch, which prompted the envoy's resignation.
Sir Kim resigned last week saying his position had become "impossible" following the leak of diplomatic cables in which he described Mr Trump's White House as "inept" and "dysfunctional".
The Mail On Sunday released further details of his correspondence, including a memorandum from May 2018 in which the ambassador suggested Mr Trump had decided to pull out of the Iran nuclear deal in an act of spite because it was agreed by his predecessor Barack Obama.