Donald J. Trump said Sunday that a Muslim judge might have trouble remaining neutral in a lawsuit against him, extending his race-based criticism of the jurist overseeing the case to include religion and opening another path for Democrats who have criticized him sharply for his remarks.
The comments, in an interview with John Dickerson, the host of CBS’s “Face the Nation,” come amid growing disapproval from fellow Republicans over his attacks on Judge Gonzalo P. Curiel, a federal judge in California overseeing a suit against the defunct Trump University, whose impartiality Mr. Trump questioned based on the judge’s Mexican heritage.
And they came as Republicans, concerned about how his remarks could harm their ability to retain control of the United States Senate and have a detrimental effect in races further down the ballot, continue to grapple with how to distance themselves from Mr. Trump’s rhetoric without alienating his die-hard voters.
Mr. Trump has called Judge Curiel, who was born in Indiana to Mexican immigrants, a “Mexican” and said he has a “conflict of interest” in the case because of Mr. Trump’s proposed border wall with Mexico. The case that Judge Curiel is overseeing is a class-action suit in which students of the for-profit operation say they were defrauded.
Mr. Dickerson asked Mr. Trump if, in his view, a Muslim judge would be similarly biased because of the Republican presumptive nominee’s call for a ban on Muslim immigrants. “It’s possible, yes,” Mr. Trump said. “Yeah. That would be possible. Absolutely.”
When Mr. Dickerson noted that there is a tradition in the United States, a nation of immigrants, against judging people based on their heritage, Mr. Trump replied: “I’m not talking about tradition. I’m talking about common sense, O.K.?”
At a recent rally in San Diego, where the suit is being heard, Mr. Trump engaged in a minutes-long attack on Judge Curiel over the suit, which cuts at the heart of the candidate’s appeal to voters as a successful businessman.
With Mr. Dickerson and, in a separate interview, with Jake Tapper of CNN’s “State of the Union,” Mr. Trump repeated not only the criticisms of Judge Curiel, but he intensified them.
“He is a member of a club or society, very strongly pro-Mexican, which is all fine,” Mr. Trump said. “But I say he’s got bias. I want to build a wall. I’m going to build a wall. I’m doing very well with the Latinos, with the Hispanics, with the Mexicans, I’m doing very well with them, in my opinion.”
The candidate’s broadside against Judge Curiel was one of the most overtly racial remarks he has made in the presidential race, and it has been roundly criticized by prominent Republicans. It also came after Mr. Trump delivered a stinging rebuke to Gov. Susana Martinez of New Mexico, the head of the Republican Governors Association and a star within her party, after she declined to appear with him at an event in her state.
The remarks exacerbated the tension that Republicans face in embracing their nominee. White, older, working-class voters comprise a large chunk of the party’s base, and Republicans need to keep the presidential campaign close in order to hold their Senate majority. But Mr. Trump has offended wide swaths of voters to whom the party must appeal amid shifts in national demographics.
The result has left Republicans to mitigate the damage by rejecting Mr. Trump’s language in one moment, but embracing his candidacy the next. An example last week was Speaker Paul D. Ryan, who endorsed Mr. Trump with lukewarm praise after declining to back him when he became the presumptive nominee. A day later, Mr. Ryan was forced to respond to Mr. Trump’s condemnation of Judge Curiel’s impartiality; Mr. Ryan rejected Mr. Trump’s comments.
On NBC’s “Meet the Press,” Senator Mitch McConnell, the majority leader, did not directly answer a question about whether the remark was racist, but said he completely disagreed with it. “All of us came here from somewhere else,” Mr. McConnell said in reference to Judge Curiel’s heritage. “That’s an important part of what makes America work.”
Senator Bob Corker of Tennessee, a Republican who had been floated as a potential vice-presidential nominee alongside Mr. Trump, said on ABC News’ “This Week” of Mr. Trump’s behavior, “I think that he’s going to have to change.” And Newt Gingrich, the former Speaker who has been among Mr. Trump’s most vocal supporters, called the remarks “inexcusable” on “Fox News Sunday.”
“This is one of the worst mistakes Trump has made,” said Mr. Gingrich, who has also been mentioned as a potential vice-presidential candidate.
But none of the three men rejected Mr. Trump’s candidacy outright. Mr. Gingrich praised Mr. Trump moments later as a quick learner. Mr. Corker suggested that Mr. Trump “has an opportunity to really change the trajectory of our country, and it’s my sense that he will take advantage of that.”
In the weeks since he vanquished his remaining two primary opponents, Mr. Trump has repeatedly turned the campaign’s focus inward — about his businesses, the Trump University lawsuit, his fights with other Republicans — and obscured hopes Republicans had of keeping a spotlight on Hillary Clinton and her email controversy or on a jobs report suggesting a slowing of the economy.
Mr. McConnell, who quickly endorsed Mr. Trump after he became the presumptive nominee in early May, has been vocal about his concern that the remarks about Hispanics will have historic implications, along the lines of those that Barry Goldwater had on the party’s ability to woo black voters after he declined to support the Civil Rights Act of 1964.
Mr. McConnell argued that the alternative to Mr. Trump — a second Clinton presidency — was worse. But he also urged Mr. Trump to stop focusing on the recent past and look to the future.
“This is a good time, it seems to me, to begin to try to unify the party,” Mr. McConnell said. “And you unify the party by not settling scores and grudges against people you’ve been competing with. We’re all behind him now. And I’d like to see him reach out and pull us all together and give us a real shot at winning this November.”