Trump reportedly made the remarks at a White House meeting on immigration on Thursday and a USA senator who attended the gathering said on Friday that the president used "vile, vulgar" language, including repeatedly using the word "s***hole".
He also took issue with Trumps reported suggestion that the United States should welcome immigrants from places like Norway, whose population is overwhelmingly white, instead of from African countries and Haiti.
The comments revived charges that the president is racist, and rocked immigration talks that were already on a tenuous footing.
Graham released a statement saying that he "said [his] piece directly" to Trump, but not addressing whether the president had insulted any countries.
He reiterated his call for ending chain migration and the lottery route to immigration.
"They have not often had the government the people deserve, but that does not make them the country the president described", Clinton wrote.
In a series of Tweets early Friday, Trump admitted to using "tough" language but denied using the term "shithole" to describe Haiti and African countries.
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He reportedly insulted Haitian and African nations by questioning why the USA would accept more immigrants from Haiti and "shithole countries" in Africa rather than places like Norway. On Friday the president tweeted that his language was "tough" but insisted he did not say anything derogatory about Haitians aside from noting it's a poor country.
Haiti said it was shocked by the reported remarks and summoned the top United States diplomat in the country, asking for an apology if the term had been used. He also blamed "both sides" after a white supremacist rally in Charlottesville, Virginia, turned violent. President Trump did not answer Ryan's question, or any of the others.
In Geneva, UN human rights spokesman Rupert Colville said: "These are shocking and shameful comments".
The word "shithole" was projected onto President TrumpDonald John TrumpHouse Democrat slams Donald Trump Jr. for "serious case of amnesia" after testimony Skier Lindsey Vonn: I don't want to represent Trump at Olympics Poll: 4 in 10 Republicans think senior Trump advisers had improper dealings with Russia MORE's D.C. hotel Saturday.
South Africans went on the social media to vent their outrage over Trump's remarks. "Ours is not a shithole country. Neither is Haiti or any other country in distress", she said.
"Why are we having all these people from s***hole countries come here?" he asked, according to multiple sources present at the White House meeting.