WASHINGTON (BLOOMBERG) - Republican leaders are piling on presumptive presidential nominee Donald Trump over his accusation that a US federal judge is treating him unfairly because the judge is of Mexican ancestry.

In the latest backlash, Senator Kelly Ayotte of New Hampshire, who's facing a tough re-election race, said Monday that Trump's "comments are offensive and wrong and he should retract them".

Senator Susan Collins, a moderate from Maine, said his remarks "are absolutely unacceptable".

John Kasich, who ran against Trump for president and governs the November battleground state of Ohio, said Trump should apologize, and former White House hopeful Marco Rubio, a Florida senator, also denounced the attacks.

The furor comes amid skepticism about whether Trump can successfully turn to a general-election strategy against Democrat Hillary Clinton after running a bitter primary race, and retain the support of Republican leaders who were slow to back him because of rhetoric that some in the party warn could permanently alienate them to ethnic-minority and women voters.

"All I'm trying to do is figure out why I'm being treated so unfairly by a judge and a lot of people agree with it," Trump said on Fox & Friends, adding that former House Speaker Newt Gingrich's condemnation of the comments this weekend was "inappropriate".

"Now all I do is a quick referral and I say it and I say it loud and clear," Trump said.

Gingrich's televised comments Sunday on Trump's "inexcusable" rhetoric grabbed headlines since he is said to be under consideration as Trump's running mate. He wasn't alone.

House Speaker Paul Ryan, who endorsed Trump just last week, said on Wisconsin radio Friday he "completely" disagreed with Trump's thinking about the judge.

Senate Majority Leader Mitch McConnell, who backs Trump, said Sunday on NBC: "I couldn't disagree more with a statement like Trump's."

Senator Bob Corker of Tennessee, another potential running mate of Trump's, said Sunday on ABC: "I don't condone the comments and we can press on to another topic."

Trump has said US District Judge Gonzalo Curiel, who is overseeing cases against the Trump University real-estate program, has an inherent conflict of interest because of his Mexican heritage as Trump proposes building a wall on the U.S.- Mexico border to curb illegal immigration. Curiel was born in Indiana.

Trump on Sunday broadened his argument by saying on CBS that it's possible a Muslim judge could treat him unfairly too, because of his proposed ban on Muslim immigration.

In an illustration of Republicans' difficulty uniting around the controversial candidate, Kasich hasn't endorsed his former rival, while Ayotte has said she "will vote for our Republican nominee, but I don't plan on endorsing in this election", and Collins has said, "I have always supported the Republican nominee for president and I would expect that I would do so this year, but I do want to see what Donald Trump does from here on out."

Curiel has declined to comment to media outlets reporting on Trump's attacks, which go back as early as February.

Last week was supposed to be the one when Trump, 69, stepped up his game as the presumptive Republican presidential nominee, honed his attacks on presumed general-election foe Clinton, and showed the world he was up to the job of US commander-in-chief. Instead, self-inflicted wounds and a blistering barrage from Clinton left him on the defensive.

The days ahead may be even tougher, with Clinton likely to get a bounce by all but securing the Democratic nomination on Tuesday, and a drumbeat of negative headlines continuing from the weekend for the billionaire political novice.

Trump started the week berating journalists at length during a press conference on May 31, this time for looking into his fundraising for veterans and whether millions of dollars in contributions promised in January had been delivered.

"I'm not changing," he declared at the event in New York. He reshuffled his campaign staff, but did little to comfort skeptical members of his own party, to say nothing of the independent voters he must attract if he wants to win in November.

By continuing to attack the media for asking questions about the amount he had raised for veterans organisations, and railing against the coverage of a lawsuit brought against his Trump University real-estate program, Trump came off less as a man making a move to the middle than one returning to the strategy that had brought him such success in the Republican primaries.

A top Trump adviser acknowledged the task in a Huffington Post interview published May 25. "There are two main challenges. One is to make the American people look at him and say, 'He can fill the chair,'" Paul Manafort said. "Does he know enough? Yes, because he knows he has more to learn. And he is constantly doing that."

Clinton wasted little time taking advantage of Trump's return to form, which seemed to accentuate the points she made in a speech in San Diego on Thursday focused on foreign policy. She blasted Trump as "temperamentally unfit" for the Oval Office.

"This is not someone who should ever have the nuclear codes, because it's not hard to imagine Donald Trump leading us into a war just because somebody got under his very thin skin," she said.

The speech, and a wave of positive publicity that followed, gave her much-needed distance from damaging headlines brought on by the release of the State Department Inspector General's report on May 25, which concluded that Clinton had violated policies on e-mail use and record keeping as secretary of state.

Trump gifted Clinton another such opportunity on Thursday night, telling the Wall Street Journal that Curiel could not be impartial because of his Mexican heritage. Clinton seized on the comments, incorporating Trump's words into her stump speech and releasing a series of biting web ads.

"Judge Curiel is as much of an American as I am. And he's as much of an American as Donald Trump is," Clinton said on Saturday. White House Press Secretary Josh Earnest, when given an opportunity to criticise Trump's comments Monday, instead pointed to criticism from Senate Republicans. He declined to say whether he thought Trump's comments were racist.

"They've had some rather pointed comment on the impact his comments could have on our judicial system," Earnest said at the White House briefing.

At least one Republican official on Monday didn't shy away from the term.

"Public Service Announcement: Saying someone can't do a specific job because of his or her race is the literal definition of 'racism,'" tweeted Senator Ben Sasse of Nebraska, an outspoken Trump critic.

"This is one of the worst mistakes Trump has made. I think it's inexcusable," Gingrich told Fox News Sunday.

"He has every right to criticise a judge. He has every right to say certain decisions aren't right and his attorneys can file to move the venue from the judge. But first of all this judge was born in Indiana. He is an American. Period," said Gingrich.

As last week wrapped up, Trump doubling down on his assertions, which, in addition to keeping his views on race front and center, also served to remind voters of the class action lawsuit against his eponymous real-estate seminar, one that New York Attorney General Eric Schneiderman on June 2 called a "scam from beginning to end".

The remarks also served to extinguish a short-lived detente between Trump and Ryan. On Thursday, Ryan finally endorsed Trump in his hometown newspaper. The declaration looked more like resignation than an affectionate embrace. On Friday, however, Ryan returned to criticising Trump after the Curiel remarks made the rounds.

While Trump's supporters continued to believe he would rebound after the lackluster week, there was also tacit acknowledgement that the candidate's message had gone off the tracks.

"Hillary's vulnerabilities are more damaging than Trump's," Roger Stone told Bloomberg Politics. "He needs to get back to exploiting them which he has done in the past with devastating effect."

Facing doubts about the discipline of his organisation, over the weekend, Trump hired Jim Murphy as his campaign's new national political director, the New York Times reported. Murphy, who worked for Bob Dole during his presidential campaigns in 1998 and 1996, replaces Rick Wiley, who was fired from that role a week ago.

The renewed unease with Trump comes as the Republican National Committee agreed to perform many of the functions traditional presidential campaigns do for themselves. While Trump, who routinely criticised big donors during the primaries and bragged that he was self-funding, has agreed to help raise funds for Republicans, the RNC will conduct much of the voter outreach, targeting, media-buying and production, opposition research, and linking with down-ballot candidates for the Trump campaign.

Clinton's campaign, meanwhile, will formally begin raising money for the general election on Wednesday, after six Democratic contests on Tuesday are almost certain to give her enough delegates to clinch her party's nomination.

But it is her forceful attacks on Trump that have really given her campaign a boost. A two-minute clip from her foreign policy speech blasting Trump posted on Clinton's Facebook page had drawn more than 3.3 million views as of Sunday.