Mr Trump also said the allegation was hurting efforts to strike a deal to protect so-called Dreamer immigrants.
The president was responding to a claim by Democratic Senator Dick Durbin that he used “vile and racist” language during a meeting on immigration reform.
The alleged remarks sparked global outrage and demands that he apologise.
“There is no other word one can use but racist,” said a UN spokesman.
On Monday, two senators who said he did indeed use the disparaging remark stood by their account of what took place.
The row broke out after Republican and Democratic lawmakers visited the president in the Oval Office on Thursday to work on a proposal for an immigration deal.
A key issue they need to agree on is what to do with an Obama-era scheme that protects some 800,000 young people who entered the US illegally as children – known as the Dreamers.
But the alleged slur was uttered during another topic for discussion – the Temporary Protected Status (TPS) given to a number of nationalities currently living in the country.
In recent weeks the Trump administration has made a series of announcements that have brought that status to an end.
Hours after the meeting, reports emerged that Mr Trump had asked: “Why are we having all these people from shithole countries come here?”
The US should be taking in migrants from countries like Norway, he is reported to have said.
Accounts suggest that when Mr Trump was told that the largest groups of immigrants with that status were from El Salvador, Honduras and Haiti, the president responded: “Haitians? Do we need more Haitians?”
On Friday, Mr Durbin said: “I cannot believe that in the history of the White House, in that Oval Office, any president has ever spoken the words that I personally heard our president speak yesterday.
“President Trump said things that were hate-filled, vile, and racist. He used those words repeatedly.”
Trump responded by saying his language was “tough” but not the language used in the news reports. He also denied he was a racist.
And on Monday he tweeted that Mr Durbin had “totally misrepresented what was said”.
He also blamed the Democratic senator for the apparent impasse over negotiations to reach a solution on the Dreamers. (Courtesy BBC)