By Steve Holland

HOLLYWOOD, Fla. (Reuters) - U.S. Republican officials began meeting on Wednesday, a day after Donald Trump's crushing victory in a New York presidential nominating contest, and said he has been winning growing acceptance within their ranks - but they want to see the billionaire do more to mend fences with the party establishment.

Trump, the front-runner to become the Republican presidential candidate in November's election, was the focus for the party's spring meeting of 168 Republican National Committee (RNC) members in Hollywood, Florida. The three-day conclave at an oceanside resort will take stock of the race for the White House and prepare for a possible contested convention in July in Cleveland.

The New York real estate mogul's win Tuesday in his home state over rivals Ted Cruz and John Kasich was an important milestone for RNC members, who said it could put him on a pathway to acquire the 1,237 delegates needed to win the nomination outright without a contested convention.

"There are a fair number of RNC members who were discounting his chances of success when we met in January and now see that he’s building a substantial lead and may in fact get to 1,237 before we get to the convention," said Steve Duprey, an RNC member from New Hampshire.

"The New York results were such an overwhelming win," Duprey said. "It's impressive. That's what I've heard people talking about."

RNC members said Trump could help improve the climate by taking steps to end the bad blood that has developed between him and the committee's leadership, including RNC Chairman Reince Priebus.

Trump has said that Cruz's harvest of delegates in Colorado, where rank-and-file Republicans did not vote or caucus, showed that the party's nominating process is "rigged." He has wondered whether Priebus, who is popular with the RNC ranks, should continue in his job if Trump is the nominee.

"I think it's time for that rhetoric to end," said Jeff Essmann, chairman of the Montana Republican Party.

Bob Kapel, the RNC member representing Washington, D.C., noted that Trump had toned down his rhetoric in his New York victory speech on Tuesday night, and said he would like to see that continue. Kapel is a delegate for former candidate Marco Rubio and now backs Ohio Governor John Kasich.

Nevertheless, Kapel said of Trump and the Republicans: "We’re about winning the White House. Obviously, I have issues with him, but our nominee will be our nominee."

South Carolina Republican Party Chairman Matt Moore said Trump's recent hiring of Rick Wiley, a Republican veteran who was former presidential candidate Scott Walker's campaign manager, was a good sign.

"It’s a positive signal despite a lack of general outreach over the past year, and I think the Trump campaign, for all the bluster, recognizes that the RNC will be an integral partner if he is the nominee and it’ll be almost impossible to win the presidency without the RNC as a partner," Moore said.

In a good sign for Trump, there appeared to be no significant move by the Republican leadership, at least at this meeting, to change the rules governing the convention. There has been talk of rewriting the rules in a way that could benefit an establishment-backed candidate like Kasich.

Trump, Cruz and Kasich all sent envoys to the meeting to explain their pathways to the nomination.

A source familiar with the situation said Wiley and other Trump representatives were meeting with Republican officials from the five Northeastern states that will hold primary elections next Tuesday: Pennsylvania, Delaware, Connecticut, Rhode Island and Maryland.

Cruz's campaign manager, Jeff Roe, held a closed-door briefing with RNC members to explain how Cruz would be a better Republican nominee than Trump, saying the U.S. senator from Texas would energize the party's grassroots supporters.

Roe dismissed talk that Cruz might now be in trouble. Cruz's pathway to the nomination is now almost entirely dependent on forcing a contested convention and winning the nomination on the second or third ballot.

"There's going to be ebbs and flows to this campaign," Roe told reporters. "This campaign is going through (the last primary elections on June 7 and likely to the convention."

(Editing by Caren Bohan and Jonathan Oatis)

Editor's note: Donald Trump regularly incites political violence and is a serial liar, rampant xenophobe, racist, misogynist and birther who has repeatedly pledged to ban all Muslims -- 1.6 billion members of an entire religion -- from entering the U.S.