President Trump is set on Wednesday to meet with Republican senators on Capitol Hill, after weeks of tumult and tension in the relationship between the president and prominent members of his own party in the Senate.

Mr. Trump was invited by Senator Rick Scott, Republican of Florida, to address a weekly lunch gathering he runs that typically draws the more conservative faction of G.O.P. senators. It was a break from norms, since a president would typically be invited by the party’s elected leader to address the entire conference at its regular luncheon on Tuesdays, or a special gathering hosted by the leadership.

But Mr. Trump has been in a simmering feud with Senator John Thune, Republican of South Dakota and the majority leader, over a range of political and policy issues. Most recently, the president has raged about Mr. Thune’s refusal to weaken the filibuster to pass legislation that would impose new voting restrictions, including substantially reducing the opportunity for voting by mail.

Mr. Thune has said repeatedly that the votes are not there to undermine the filibuster or to push through the voting legislation, known as the SAVE America Act, and test votes have shown that to be the case.

Mr. Scott, who lost badly to Mr. Thune in his bid for majority leader in 2024 after pitching himself as the Trump-aligned candidate, said he had been speaking to the president on the phone last Friday about a number of issues, including the voting bill, when he suggested that the president come to the meeting.

“I just bring people to lunch and create a conversation, and I think there’s a greater chance something good will happen,” said Mr. Scott, who said he hoped Republicans would also discuss a plan to avoid a government shutdown at the end of September. But, he added, Mr. Trump “continues to want to pass the SAVE America Act, and there’s other issues — cost of living, stuff like that.”

Speaking to reporters in Pennsylvania on Tuesday, Mr. Trump confirmed that the election bill that he has called critical to guarding against Republican losses in November would be a central focus.

“Well, we’re just going to talk about SAVE America,” he told reporters in Reading, Pa., adding: “We have to pass it. So we’re going to have to talk about that, and many other things.”

Asked about Mr. Thune’s skepticism that the bill could pass, Mr. Trump gently pressured the majority leader to round up the necessary support.

“That’s what being a leader is about,” he said, adding, “John is a leader, and hopefully he can get the votes.”

The dispute over the legislation is resurfacing amid mounting bitterness between Mr. Trump and Senate Republicans, many of whom have been livid at the president’s decision to back successful primary challenges to two Republican senators he considered disloyal.

It has also exposed rifts among Senate Republicans themselves about the voting legislation, which does not have sufficient support from Democrats to overcome the 60-vote threshold required to move most bills through the Senate.

Mr. Thune has said that there is no practical path to move the measure. Senator Bill Cassidy, Republican of Louisiana and one of the bill’s co-sponsors, said on Monday that “it doesn’t have the votes, and so it’s time to talk about something else.”

But Senator Mike Lee, Republican of Utah, suggested that his colleagues needed to fight harder for the legislation. In a social media post on Tuesday, he criticized Mr. Thune for suggesting that senators needed to tell Mr. Trump that the bill was dead.

“At tomorrow’s meeting between President Trump and Senate Republicans, do you want your senators to advocate (1) FOR, or (2) AGAINST trying to pass the SAVE America Act?” he wrote.

Mr. Thune later batted down the criticism with a swipe of his own, suggesting that Mr. Lee was trafficking in social-media-driven delusion rather than truth.

“I appreciate that it’s his prerogative to communicate how he wants to communicate, but at the end of the day, I have to deal with reality,” he told reporters. “And sometimes the alternative universe that is X doesn’t reflect the facts on the ground.”

Mr. Thune also suggested that it could be beneficial for Mr. Trump to hear from other senators about the legislation’s grim chances.

“Our conference is pretty well aware and conscious of where the votes are on these issues and so, yes, it is always helpful if others would speak up and it’s not just me,” Mr. Thune told reporters. “I’ve made that point many times, but it is always good to have it reinforced by others.”

Other Republican senators criticized Mr. Lee for inflating the prospects for the legislation and raising the president’s hopes when it has no chance to become law without changes to the filibuster that Mr. Thune has pledged to oppose.

“Mike’s a smart guy, so it must be some other motivation,” said Senator John Cornyn, Republican of Texas, who has been bickering with Mr. Lee about the bill on social media. “My guess is that this is mainly designed to eliminate the filibuster, to get us in a position where we have to eliminate the filibuster, to give the president what he wants. And that’s not going to happen.”

Senator Thom Tillis, Republican of North Carolina, said the filibuster debate was preventing Republicans from making more constructive use of their time before the midterm elections, and should be abandoned.

“We are going down a path that is unproductive, and every minute we spend on it, we are not spending on something that could get my colleagues re-elected, which is the No. 1 priority for me between now and November,” Mr. Tillis said.