Republican senators who met with Pete Hegseth, President-elect Donald Trump’s pick for Defense secretary, are all in for the former Fox News co-host who is trying to dispel concerns about a 2017 sexual assault complaint that resulted in no charges.

Mr. Hegseth, an Army combat veteran, was escorted into the Capitol on Thursday by Vice President-elect J.D. Vance to meet with Republican senators and talk about his nomination.

Mr. Barrasso, Wyoming Republican, and rising No. 2 Senate Republican, said the two had an “excellent discussion about the need for America’s military to remain the best in the world.”

“That means taking care of our service members, equipping them with the latest technology and focusing on making our military the most lethal force on the planet,” Mr. Barrasso said in a statement. “Pete pledged that the Pentagon will focus on strength and hard power — not the current administration’s woke political agenda.”

Mr. Hegseth’s meetings at the Capitol ended minutes before another Trump nominee, former Rep. Matt Gaetz, withdrew from consideration for attorney general amid growing criticism over allegations of sexual misconduct with a minor and paying women for sex.

On Thursday, a police report revealed that a California woman told police that she was sexually assaulted by Mr. Hegseth in 2017 after he took her phone and blocked her exit from a hotel room. He told police at the time that it was consensual, and denied he did anything wrong. No charges were filed.

His lawyer, Timothy Palatore, said he paid the woman in 2023 to stop the threat of a lawsuit.

Asked about the matter at the Capitol on Thursday, Mr. Hegseth told reporters “as far as the media is concerned, it’s very simple. The matter was fully investigated, and I was completely cleared, and that’s where I’m gonna leave it.”

Sen. Markwayne Mullin, Oklahoma Republican and member of the Armed Services Committee, defended Mr. Hegseth against the police report, saying “it’s completely taken out of context” and he thinks Mr. Hegseth will still get confirmed. 

Sen. Tim Kaine, Virginia Democrat and also a member of the Armed Services Committee, said “the Gaetz decision just really puts the spotlight heavily on the Sec. Def. nominee.”

And Sen. Mark Kelly, Arizona Democrat and member of the Armed Services Committee, said the pressure is on Mr. Hegseth to get confirmed because “we want serious people who are qualified, especially in the job of being the Secretary of Defense, managing perhaps one of the biggest enterprises on the planet.”

Republican Sens. Bill Hagerty and Marsha Blackburn, both of Tennessee, also met with Mr. Hegseth. Mr. Hagerty called the meeting “outstanding,” while Ms. Blackburn called him a “well-qualified nominee.” 

“Pete knows that the Defense Secretary’s job is to empower the men and women of our military to carry out their patriotic duty, not consign them to serve as political pawns in a broken Washington,” Mr. Hagerty wrote on X Thursday.

Sen. Roger Wicker, ranking Republican member of the Senate Armed Services Committee, which will be in charge of vetting Mr. Hegseth’s position, said his meeting with him was “brief and very helpful.”

• Lindsey McPherson contributed to this report.