Senator Susan Collins, Republican of Maine, said she had privately questioned Pete Hegseth on both policy issues and the misconduct allegations against him but would not decide whether to back President-elect Donald J. Trump’s pick to lead the Pentagon until after a thorough vetting.

“I pressed him on both his position on military issues as well as the allegations against him,” Ms. Collins told reporters after a private meeting with Mr. Hegseth that lasted well over an hour. “I don’t think there was anything that we did not cover.”

She said she would not be coming to a decision about Mr. Hegseth’s bid to lead the Pentagon until after an F.B.I. background check on him was complete and he had undergone a confirmation hearing, which the Senate Armed Services Committee is expected to hold in January.

Ms. Collins, who will chair the powerful Appropriations Committee in the next Congress, is one of the few Republican senators to voice concerns publicly about Mr. Hegseth after reports that detailed allegations of sexual assault and harassment of women in the workplace, public drunkenness and fiscal mismanagement.

She said she also used her time with Mr. Hegseth to press him on policy matters, including defense procurement reforms, the role of women in the military, sexual assault in the military, Ukraine and NATO.

Ms. Collins characterized the session as a “good, substantive discussion.”

But it was clear that Mr. Hegseth had not yet won her support. Afterward, he told reporters that he had no idea how Ms. Collins would eventually come down on his nomination.