President Trump is adding to the mounting pressure on House Republicans to impeach President Biden by calling on any Republican who would not vote for impeachment to be replaced.

During a campaign event at Erie, Pennsylvania, on Saturday, Mr. Trump demanded: “Any Republican that doesn’t act on Democrat fraud should be immediately primaried and get out.”

“If they’re not willing to do it, we’ve got a lot of good, tough Republicans around. People are going to run against ‘em, and people are going to win,” Mr. Trump said. “And they’re going to get my endorsement every single time. They’re going to win ‘cause we win almost every race when we endorse.”

That was markedly more aggressive than Speaker McCarthy’s comments on a potential impeachment inquiry last week, adding to the pressure Republicans are receiving to launch such an inquiry of the president over corruption and bribery allegations related to his troubled son Hunter’s business dealings with Ukrainian and Chinese business interests

Last week, Mr. McCarthy told Fox News, “This is rising to the level of an impeachment inquiry which provides Congress the strongest power to get the rest of the knowledge and information needed.”

Although Mr. McCarthy later appeared to qualify during a press availability, explaining that “I wasn’t announcing it,” it’s clear that he sees the House as on a trajectory toward impeachment.

“If evidence continues to rise to the level of an impeachment inquiry, House Republicans will act,” Mr. McCarthy said in a tweet.

While House Republicans pushed for impeachment ahead of the August recess, which began at the end of last week, Democrats have criticized the effort as being aimed at boosting Mr. Trump’s re-election chances.

“It’s clear that Donald Trump is the real Speaker of the House,” the Democratic National Committee chairman, Jaime Harrison, said in a statement. “He has made sure the House majority is little more than an arm of his 2024 campaign, and Kevin McCarthy is happy to do his bidding.”

Mr. Biden has denied the allegations against him.

Some Republicans in the Senate have also expressed concerns that a focus on impeachment may not be a winner electorally and could derail business in Congress.

“Staying focused on the future and not the past is in my view the best way to change the direction of the country and that’s to win an election,” the Senate Republican whip, John Thune, told reporters Tuesday.  

The chairwoman of the Senate Republican Policy Committee, Joni Ernst, told reporters that she was focused on the National Defense Authorization Act and that she would prefer to keep focused on passing appropriations bills.

“I really want to see it get done and I want a bipartisan deal between the House and the Senate. I think that’s what we’re focused on,” Ms. Ernst told reporters. “We need to get our bills done, too. So, that’s what we’re going to focus on in the Senate.”

Others in the upper chamber have been more aggressive in terms of impeachment rhetoric, calling for the impeachment of not only Mr. Biden but other officials in his administration as well.

“I believe the House should pursue three separate impeachment inquiries into Alejandro Mayorkas, Merrick Garland, and Joe Biden,” Senator Cruz said in a statement. “Each deserves a chance to present a defense to the serious allegations they face.”

It’s unclear whether House Republicans currently have a majority prepared to vote to impeach. Previous impeachment efforts, like those brought by Congresswoman Lauren Boebert, have been sent to the committee by leadership.

With Messrs. Trump and McCarthy both pushing for impeachment, though, whatever Republican House moderates may have been reluctant to vote for impeachment previously will face the looming threat of rebuke by Mr. Trump and a possible primary challenger.