Trump's comments Thursday came as two senators presented details of a bipartisan compromise that would extend protections against deportation for hundreds of thousands of young immigrants - and also strengthen border protections, as Trump has insisted.
President Trump has since denied using vulgar language at his immigration meeting.
In a tweet, Clinton denounced Trump's remarks, which were made in a private meeting with lawmakers on Thursday, saying that Friday should be a day of remembrance for the 2010 natural disaster in Haiti.
The president tweeted later on Friday: "Never said anything derogatory about Haitians other than Haiti is, obviously, a very poor and troubled country". "What was really tough was the outlandish proposal made".
Graham said he pushed back at the president - an account that was backed up by Illinois Democratic Sen.
She said asking if Trump is racist is not enough, that people need to do something that will have an "economic impact". In an editorial, the local Daily Maverick called the comments "a new low", adding, "Casual Friday at the White House is soon to include hoods and tiki torches at this rate".
"Following comments by the President", Graham said in the statement, "I said my piece directly to him yesterday..."More news: Forecast: Expect snow, then more cold weather
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Senator Durbin said that after yesterday's meeting any hope for a deal "died".
Durbin said Graham immediately objected to the president's comments.
In 2017, as president, he came under fire for saying there were "many fine people" on both sides of the Charlottesville protest which included white supremacists. I thought about my own family.
"Each Charge or Ambassador should note what a great honor it is to be in their post and how much they value the relationship with the people of the nation they are representing (use nation's name)", the guidance reads.
"Why are we having all these people from shithole countries come here", Trump reportedly said. Never said "take them out".
Despite Trump's denial, the comments quickly drew global condemnation and Florida lawmakers joined in the chorus of calling the president out for what they deemed as "insensitive" remarks.
Echoed Republican Sen. Susan Collins of Maine: "These comments are highly inappropriate and out of bounds and could hurt efforts for a bipartisan immigration agreement".