(Reuters) - A promise that U.S. Republican front-runner Donald Trump will adopt a more presidential campaign style does not signal a retreat from 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 rival Republican candidate Ted Cruz’s accusation that the real estate mogul had lied about his policies on immigration to “fool gullible voters.” The tussle over Trump’s style and substance preceded Tuesday’s Republican and Democratic nominating contests in Pennsylvania and four other Northeastern U.S. states: the next chapter in 2016’s drawn-out selection of the candidates for November’s presidential election. Cruz seized on Manafort’s comments at a closed-door meeting of top Republican officials in Florida on Thursday that Trump, 69, 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 Sunday.” The adviser said Cruz, a 45-year-old U.S. senator from Texas who is Trump’s closest rival, was trying to distract voters from his own difficult path to the nomination. Ohio Governor John Kasich, 63, is also vying to be the Republican candidate. But, despite Manafort’s promise of a more restrained tone, Trump has continued to employ insulting nicknames at rallies, on Saturday referring to Cruz as “Lyin’ Ted.” The billionaire New Yorker has alarmed some senior party figures with unflattering descriptions of Mexicans, a pledge to immediately deport millions of illegal immigrants and a proposed temporary ban on Muslims entering the country, among other things. The rhetoric has drawn protesters to Trump rallies, sometimes culminating in scuffles. On Sunday, the Connecticut State Police arrested a 20-year-old man, saying he had posted a threat on Twitter to bomb an upcoming Trump rally. On Tuesday - one week after Trump’s crushing win in New York’s primary election - Pennsylvania, Maryland, Delaware, Connecticut and Rhode Island will hold their primaries.  Democratic front-runner Hillary Clinton’s campaign says the former secretary of state now has an essentially insurmountable lead over rival Bernie Sanders. The 74-year-old U.S. senator from Vermont has no plans to drop out of the race, according to his staff, who are counting on defying pollsters with some surprise wins on Tuesday. Trump is working to accrue the 1,237 delegates to the July 18-21 Republican National Convention needed to win the nomination outright. That would avert a contested convention, in which Cruz, Kasich or a dark-horse establishment figure could win the nomination on a second or subsequent ballot. Manafort predicted Trump would win the nomination on the first ballot at the Cleveland convention. Trump already has at least 844 delegates committed to him, according to the Associated Press. Cruz has 543 and Kasich has 148. In the five Northeastern states, 118 delegates will be at stake. Pennsylvania will also choose 54 delegates not bound to any candidate.  Trump has won more states overall than Cruz has, but the Texan has tried to keep Trump from winning the needed delegates by using selection rules that vary by state. In Colorado, for example, delegates were picked without a popular vote. “He’s trying to say the process doesn’t matter. He’s trying to say voting doesn’t matter,” Manafort said of Cruz on Sunday. “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. “We’re not going to let that happen,” Manafort said.  State nominating contests continue through June. Also on Sunday, Republican National Committee Chairman Reince Priebus played down conservative billionaire Charles Koch’s comment that “it’s possible” Clinton, 68, 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,” Priebus said. “And I think that’s going to be a very powerful case that we’re going to be able to make as a party.” Democrats, including Clinton, have criticized Koch and his brother, David Koch, for using their wealth and a huge funding network they helped organize to support politicians, usually Republican ones, who reflect their opposition to government regulation of industry. The Clinton campaign was not pleased with Koch’s faint praise. A response to Koch’s comments posted on Clinton’s Twitter account said, “Not interested in endorsements from people who deny climate science and try to make it harder for people to vote.” 