Also on Tuesday, House Speaker Paul Ryan, the highest elected GOP official, told reporters that "claiming a person can't do their job because of their race is sort of like the textbook definition of a racist comment. I think that should be absolutely disavowed. It's absolutely unacceptable."
Trump has said that U.S. District Judge Gonzalo Curiel, who is from northwest Indiana, can't preside fairly over a case involving Trump University because the judge is of Mexican heritage and Trump wants to build a wall between the U.S. and Mexico.
Ryan endorsed Trump only last week after a lengthy delay, just before the judge controversy flared, and affirmed that stance again Tuesday even while he was unstinting in his criticism of Trump's comments. "But do I believe Hillary Clinton is the answer? No, I do not," Ryan said.
Nineteen Republicans have denounced Trump for his comments about the federal judge, three of them have said they won't support him.
Kirk also raised questions about the businessman overseeing the nation's nuclear weapons as commander in chief.
Kirk's full statement read: "I have spent my life building bridges and tearing down barriers-not building walls. That's why I find Donald Trump's belief that an American-born judge of Mexican descent is incapable of fairly presiding over his case is not only dead wrong, it is un-American. As the Presidential campaign progressed, I was hoping the rhetoric would tone down and reflect a campaign that was inclusive, thoughtful and principled. While I oppose the Democratic nominee, Donald Trump's latest statements, in context with past attacks on Hispanics, women and the disabled like me, make it certain that I cannot and will not support my party's nominee for President regardless of the political impact on my candidacy or the Republican Party. It is absolutely essential that we are guided by a commander-in-chief with a responsible and proper temperament, discretion and judgment. Our President must be fit to command the most powerful military the world has ever seen, including an arsenal of thousands of nuclear weapons. After much consideration, I have concluded that Donald Trump has not demonstrated the temperament necessary to assume the greatest office in the world."
Given my military experience, Donald Trump does not have the temperament to command our military or our nuclear arsenal.— Mark Kirk (@MarkKirk) June 7, 2016
In response, Tammy Duckworth, who looking to unseat Kirk, released a response to Kirk which read, in part: "What took so long? Apparently for Mark Kirk, it's acceptable to refer to Mexicans as rapists; to propose banning Muslims from entering the country; to call women fat pigs and dogs; to mock a reporter's disability; and to insult just about everyone who doesn't look like Donald Trump. Until today, and for nearly a year, Kirk was fine with all of that."
GOP SUPPORT FOR TRUMP
The flap comes as Republicans are struggling to close ranks behind Trump, and complicates those efforts.
Other Capitol Hill Republicans joined Ryan in heaping denunciations on Trump, yet in some cases continuing to back the billionaire in an awkward, arm's-length embrace.
Sen. Tim Scott, R-S.C., the only black Republican senator, called Trump's comments on the judge "racially toxic" yet said, "He needs to get onto the general election and we need to win."
"From what I know about Trump, he's not a racist. But he does make a lot of outrageous statements. And I think he ought to tone it down a little bit," said Sen. Orrin Hatch, R-Utah, while calling on the media to give Trump "leeway" for what he called a "mistake."
"Let's face it, meet the old Trump, just like the new Trump," said Sen. Jeff Flake, R-Ariz., who has long opposed the billionaire's candidacy. "We've got what we've got. That's not somebody who can win the White House."
"Where there's no talk of a convention challenge or anything else, this might spur it," Flake said of Trump's comments on the judge.
Democrats immediately ridiculed Ryan for denouncing Trump's comments as racist yet continuing to back his candidacy.
"Paul Ryan continues to endorse someone who spews racist rhetoric - the 'textbook definition' of a coward more concerned with partisan politics than the good of the country," said Meredith Kelly, spokeswoman for the Democratic Congressional Campaign Committee.