Trump's toned-down demeanor doesn't mean policy change

April 24 (Reuters) - Republican Donald Trump's more presidential style on the campaign trail is not a signal that he will retreat on core policies such as his pledge to build a wall on the Mexican border, his top adviser said on Sunday.

Senior Trump aide Paul Manafort dismissed accusations by rival Republican Ted Cruz that the real estate mogul had lied about his policies on immigration to "fool gullible voters."

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Cruz said that after Manafort told a closed-door meeting of top Republican officials last week that the party's White House front-runner would temper the image he has projected so far, saying the "part that he's been playing is now evolving."

"I never said Trump wasn't going to build a wall. I never said Trump was going to change any of his positions," Manafort said on Fox News on Sunday.

Manafort said Cruz was trying to distract from his tough path to the nomination, especially with primary elections coming in Pennsylvania and other states where polls show Trump ahead.

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He predicted his candidate would win on the first ballot at the Republican National Convention in July. Trump has won more states than Cruz has, but Cruz hopes to keep him from earning the 1,237 delegates needed to secure the nomination at the Cleveland gathering.

"He's trying to say the process doesn't matter. He's trying to say voting doesn't matter. He's trying to say all that matters is to destroy the party and see who can pick up the pieces on a second, third or fourth ballot," Manafort said of the Texas senator. "We're not going to let that happen."

Also on Sunday, Republican National Committee chairman Reince Priebus played down conservative billionaire Charles Koch's comment that "it's possible" Democratic front-runner Hillary Clinton would make a better president than the Republicans in the race.

"Charles, in the past, has gone out of his way to make the case for him being a little bit less partisan than people would expect," Priebus said on ABC.

"It's going to come down to four to eight more years of Barack Obama and Hillary Clinton or a different direction. And I think that's going to be a very powerful case that we're going to be able to make as a party," Priebus said.

(Reporting by Emily Stephenson; Editing by Tom Heneghan)