COLUMBUS, Ohio — President Trump acknowledged a “probably tougher” path to retain GOP control of the House at the state party’s annual dinner here, injecting some political reality into his standard rhetoric that boasts of a “red wave” in November.

Trump traveled to the Ohio capital Friday to rally a state party that has faced internal strife, most notably the high-profile rift between the president and the state’s governor, Republican John Kasich. The governor skipped Friday’s dinner.

“I think in the Senate, we’re doing really well. . . . We’re going to win a lot of seats,” Trump said in his headliner speech. He said Sen. Rob Portman (R-Ohio) listed “name after name” of Republican candidates “who are doing great” as they challenge Democratic senators.

But, Trump noted, “the House is probably tougher.” He blamed the internal House Republican conference rules that impose a six-year term limit on holding chairmanships, which Trump speculated was driving several veteran lawmakers out of office. Eight House GOP chairmen are retiring this year.

“I guess it gets other people up there, but in the meantime, we have a lot of chairmen that have no choice” but to leave, Trump said.

The bulk of the 54-minute speech was Trump’s standard-fare campaign stump speech — with heavy focus on the economy, immigration and trade — but delivered in a much more subdued tone to fit the atmosphere of the formal gala dinner.

At the start of the dinner, Trump singled out the “great” Rep. Jim Jordan (R-Ohio), who has come under fire amid accusations that he turned a blind eye to reports of abuse by wrestlers at Ohio State University by the team’s former doctor when he served as a coach there.

“Don’t ever wrestle him,” Trump said, praising Jordan’s wrestling skills. “People don’t know this about Jim — he was one of the best wrestlers ever in college wrestling.”

He slammed Democratic gubernatorial candidate Richard Cordray, the former director of the Consumer Financial Protection Bureau who Trump derided as a “far-left candidate” who was “groomed by Pocahontas” — a racial slur in reference to Sen. Elizabeth Warren (D-Mass.), for whom the consumer agency was a brainchild.

And Trump rolled out his standard “he voted no” line against Democratic Senate candidates, this time against Sen. Sherrod Brown (D-Ohio), who is being challenged by Rep. James B. Renacci (R) this November.

“Sherrod voted no on our tax cuts. He voted no on repealing Obamacare. He voted no on Neil Gorsuch. How do you do that?” Trump said. Brown, who announced earlier Friday that he would vote against Supreme Court nominee Brett M. Kavanaugh, “voted for the liberal Obama judges who want to take away your Second Amendment” rights, Trump asserted.

He added: “Maybe I’m wrong. I don’t see Ohio as liberal. Are you liberal?”

The crowd responded, “No!”

Trump did not mention Sen. John McCain (R-Ariz.), whose family announced earlier Friday was ending medical treatment more than a year after he was diagnosed with glioblastoma, an aggressive form of brain cancer.

Kasich also went unmentioned by Trump. Trump and Kasich have been feuding since they faced off in the 2016 GOP presidential primary, and they have yet to bury their hatchet. The Ohio governor continues to be one of the most pointed critics of the president in the Republican Party.

This month’s closely contested special House election in a suburban Columbus-area district, in which Republican Troy Balderson was declared the winner Friday, triggered a war of words between Kasich and Trump. The president tweet-blamed the governor for the GOP’s narrow margin in the heavily Republican district. Kasich responded in kind, with a GIF of Russian President Vladimir Putin laughing.

Kasich said this week that he would not be attending the annual state party dinner here and would instead be accompanying one of his twin daughters to college.

Earlier Friday, Trump and first lady Melania Trump tried to project a unified front in a week in which the guilty plea of his former longtime attorney, Michael Cohen, put the president’s alleged affairs back in the spotlight. Cohen said in federal court Tuesday that he, in coordination with then-candidate Trump, arranged to pay off two women to keep them quiet about the alleged dalliances before the November 2016 election.

The president and the first lady toured a neonatal intensive-care unit at Nationwide Children’s Hospital here, walking down a small hallway of curtained-off rooms where infants, born to opioid-addicted mothers, were being treated. The first couple then spent some time in a play area at the hospital with older children. Melania Trump worked on drawings, and the president looked impressed at a young girl who showed him some gymnastics tricks.