Pete Hegseth, President-elect Trump's nominee for secretary of defense, is ramping up his pitch to lead the Pentagon with back-to-back meetings on Capitol Hill.

Since his nomination, Hegseth has been meeting privately with senators in Washington, D.C., in an effort to earn their support ahead of his confirmation hearing next year.

Hegseth was back on the Hill for a second day on Wednesday, meeting first with incoming Sen. Roger Wicker, R-Miss., who is set to be the Armed Services Committee chair, ahead of a crucial meeting with incoming Senate Majority Leader John Thune, R-S.D. 

Following his private meeting with Thune, Hegseth told reporters that "the meeting was great." 

The nominee has faced a series of drinking and sexual misconduct allegations, all of which he has denied, since being tapped for the top administration role.

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An email was recently leaked from Penelope Hegseth, Pete Hegseth's mother, where she was critical of his past relationships with women. However, she joined "Fox and Friends" Wednesday morning to set the record straight and "tell the truth to the senators on the hill, especially our female senators."

Penelope Hegseth said she wrote the email in an impassioned moment after her son's divorce, but apologized hours after sending it. Hegseth's mother also said she did not believe any of the accusations against him.

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Multiple sources confirmed to Fox News that Trump is reportedly considering nominating Republican Florida Gov. Ron DeSantis as Defense Secretary in place of Hegseth amid the allegations against him.

But Hegseth brushed off the potential replacement, telling reporters that he spoke with Trump on Wednesday morning, who reportedly told him to "keep going, keep fighting."

"Why would I back down?" Hegseth said. "I have always been a fighter. I am here for the war fighters."

Hegseth added that he would be "meeting all day with senators."

In an op-ed for the Wall Street Journal, published Wednesday afternoon, Hegseth outlined his military service and his time working with veterans after leaving the Army.

"I’ve been through a lot: combat tours, job changes, divorces and family challenges," Hegseth wrote, before bashing the press for using "anonymous sources to try to discredit" him.

"Talk to those who served with me in Guantanamo Bay, Iraq, Afghanistan or the National Guard. They support me, and I’m honored by that," Hegseth wrote. "I have never backed down from a fight and won’t back down from this one. I am grateful President-elect Trump chose me to lead the Defense Department, and I look forward to an honest confirmation hearing with our distinguished senators—not a show trial in the press.  

Fox News' Bret Baier, Paul Steinhauser and Bill Melugin contributed to this report.