By Richard Cowan and Steve Holland

WASHINGTON (Reuters) - Bowing to pressure from fellow Republicans, Donald Trump said on Tuesday he would no longer talk about a Mexican-American judge after U.S. House Speaker Paul Ryan denounced the presidential candidate's criticism of the jurist as textbook racism.

But Trump refused entreaties from party leaders to disavow his charge that U.S. District Judge Gonzalo Curiel was showing bias because of his Mexican heritage and should recuse himself from a lawsuit alleging fraud at Trump's defunct Trump University real estate training school.

Trump said in a statement that his previous remarks about Curiel had been misconstrued.

"I do not feel that one’s heritage makes them incapable of being impartial, but, based on the rulings that I have received in the Trump University civil case, I feel justified in questioning whether I am receiving a fair trial," the presumptive Republican nominee said. Trump added that he did not plan to comment further on the matter.

Trump had been suggesting that Curiel's heritage was influencing the judge's opinion about the case because of Trump's campaign rhetoric about illegal immigration. Trump has pledged to seal the U.S.-Mexico border with a wall, and has said Mexico is sending rapists and drug dealers to the United States.

Ryan, the country's top elected Republican, blasted Trump's comments, which have threatened to disrupt Republicans' already rocky efforts to unite behind the candidate.

"I regret those comments that he made. 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," Ryan told reporters.

The controversy over Trump's attacks on the judge has set back his efforts to try to unify the Republican party behind him ahead of the Nov. 8 general election when he will face off against presumptive Democratic nominee Hillary Clinton.

Speaking to supporters at the golf club he owns in the hilly suburbs of New York later on Tuesday, Trump laid out his vision for the meaning of his campaign slogan "America First," talking about its implications for trade, energy, financial regulation and tax policies.

Breaking with his usual practice of speaking off the cuff, Trump read from a teleprompter and left without taking questions from reporters.

Ryan, who endorsed Trump last week after initial misgivings, said he still supported his candidacy, saying Trump would be preferable to Clinton.

Behind the scenes, Trump has been pressured from friends and family to back down, fearful of the damage that may be done to his prospects in the general election, a source close to the Trump campaign said.

New Jersey Governor Chris Christie, a potential Trump vice presidential running mate, was spotted at Trump Tower in New York before Trump's statement was issued. Christie earlier in the day defended Trump as "not a racist."

"Some of his friends and family have talked to him and asked him to drop it and so far he won’t do it," the source said, speaking before Trump's statement was issued. "Everybody is mystified about why he would keep doing it."

HIGH ANXIETY

Ryan's emphatic rejection of Trump's comments showed anxiety among party leaders about their ability to hang on to control of the U.S. Congress in November if voters trounce Trump and also punish candidates for other offices on the Republican ticket.

Ryan's counterpart in the Senate, Mitch McConnell, said Trump should stop attacking minority groups.

"My advice to our nominee is to start talking about the issues that the American people care about, and to start doing it now," the Senate Republican leader told reporters.

"In addition to that, it's time to quit attacking various people that you competed with or various minority groups in the country and get on message."

Senator Mark Kirk, an Illinois Republican who said back in March he would support whoever turned out to be the Republican nominee, said on Tuesday he could not support Trump because he did not have the “temperament necessary” for the White House.

Kirk condemned Trump’s comments on Curiel as “dead wrong” and “un-American.” Kirk is seeking re-election in November.

During the Republican primary campaigns, in which Trump vanquished 16 opponents with a stream of insults to rivals and inflammatory comments about Muslims, immigrants and women, establishment Republicans squirmed over the prospect of the former reality television host becoming their standard-bearer.

But many, seeing no alternative, have reconciled themselves to a Trump run for the White House.

'UNFAIR POSITION'

Trump's continuing practice of making explosive remarks about racial, religious and gender issues is making Republicans, including those who have embraced him, uncomfortable.

With greater scrutiny of Trump now that he is set to formally win the Republican presidential nomination at the party's July convention in Cleveland, there are concerns about the party's ability to maintain control of the House of Representatives and Senate.

"Trump's continuing missteps, punctuated by his outrageous and indefensible comments about Judge Curiel, make that goal much more difficult to achieve," said Lanhee Chen, a senior adviser to former presidential candidate Marco Rubio and a senior fellow at the conservative Hoover Institution.

(Reporting by Richard Cowan and Steve Holland; Additional reporting by David Morgan, Susan Heavey and Doina Chiacu; Editing by Frances Kerry and Howard Goller)