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MILWAUKEE — Donald J. Trump called for Gov. John Kasich of Ohio to drop out of the Republican primary contest, saying that Mr. Kasich “should not be allowed to run.”

Mr. Trump said on Sunday that Mr. Kasich, who has so far finished first in just one primary — in his home state, Ohio — could ask to put his name under consideration for the nomination at the Republican convention in Cleveland in July. But he said Mr. Kasich was siphoning votes from him and called on the Republican National Committee to urge him to drop out.

“Kasich shouldn’t be allowed to continue, and the R.N.C. shouldn’t allow him to continue,” Mr. Trump told a small group of reporters at Miss Katie’s Diner here.

Mr. Trump, who is struggling to make up ground against Senator Ted Cruz of Texas in Wisconsin, which votes on Tuesday, argued that Mr. Kasich had no chance of winning the 1,237 delegates required to earn the party’s nomination and should therefore end his 2016 bid.

“Rand Paul could’ve stayed in and he had nothing, Marco Rubio could have stayed in, Jeb Bush could have stayed in,” Mr. Trump said, listing some of his previous Republican rivals who had since ended their campaigns. “They all could have stayed in. They could have just stayed in. That’s all he’s doing.”

Mr. Trump, who last week met with R.N.C. officials in Washington, said he had been mentioning his concerns to committee officials, including Reince Priebus, the party’s chairman.

“I said, ‘Why is a guy allowed to run?’” He said. “All he’s doing is just he goes from place to place, and loses, and he keeps on running.”

Mr. Trump added that he told the R.N.C. that the situation was “very unfair.”

“He doesn’t have to run and take my votes,” Mr. Trump said.

Chris Schrimpf, a spokesman for Mr. Kasich, said in a statement that both Mr. Cruz and Mr. Trump were unlikely to secure the necessary delegates to win the Republican nomination — and instead called for Mr. Trump to drop out.

“Ted Cruz also has no possibility of accumulating enough delegates and Trump also will not receive a majority of delegates before the convention,” Mr. Schrimpf said. “Since he thinks it’s such a good idea, we look forward to Trump dropping out before the convention. Trump living up to his own self-declared standard is best for the party since he will lose the White House by a historic margin to Hillary Clinton and also cause Republicans to lose control of the Senate.”