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A prominent Republican senator on Wednesday called for sexual harassers in Congress to be outed.

“Name them,” Sen. Lindsey Graham, R-S.C., told reporters. “Just get it out. Lay it out. Change the rules so people can come to work without being harassed. Those who do these things need to be held accountable.”

Graham’s comments come one day after California Rep. Jackie Speier testified that at least two sitting members of Congress -- one from each party -- have been the subjects of rampant sexual harassment complaints.

Without naming names, Speier said she’d heard stories of victims having their “private parts grabbed on the House floor.”

Speier said Wednesday that she is barred from identifying one lawmaker because of a non-disclosure agreement. She said she won’t name the other because the victim asked her not to.

During a news conference introducing her bill to overhaul the process for reporting sexual harassment, Speier said she is “here to protect the victims.”

At Tuesday’s hearing, Virginia Republican Barbara Comstock said she’d heard a story about a member of Congress telling a staffer to bring work material to his house. When she got there, she said, he exposed himself to her.

The staffer quit.

“What are we doing here for women, right now, who are dealing with someone like that?” Comstock asked at the hearing.

Graham, who on Monday called on Alabama Senate candidate Roy Moore to step aside after a new accuser came forward alleging Moore sexually assaulted her when she was a teen, acknowledged that sexual harassment in Congress needs to be addressed.

Lindsey Graham

(REUTERS)

“It’s just rude. It’s crude. I wouldn’t want my sister… wouldn’t (want) my nieces to go through this,” he said. “I wouldn’t want a young woman to experience that kind of behavior just, you know, by participating in their government.”

During the past few weeks, stories of sexual harassment and gender hostility across many industries have been dominating the news. Multiple incidents out of D.C. and other state houses have shed light on the difficulties victims face when trying to report their accusers.

About 1,500 former Capitol Hill aides have signed an open letter to House and Senate leaders demanding that Congress put in place mandatory harassment training. They’re also calling to revamp the Office of Compliance, a small office that deals with these complaints and that few knew even existed.

“Staffers who do decide to pursue a complaint face an opaque and burdensome process,” Kristen Nicholson, director of the Government Affairs Institute, who served as chief of staff to Rep. Jim Langevin, D-R.I., from 2001-2017, wrote in an editorial.

“Hill offices are small and run largely as members see fit,” she said, adding there’s no HR department with whom to lodge a confidential complaint and that staffers are “conditioned” against saying anything that might make their boss or even the institution look bad.

After a while, offenses are seen more as an occupational hazard.

“These notions become so ingrained they stay with most of us long after we’ve left the Hill,” Nicholson said.

Earlier this month, The Associated Press reported on one current and three former female lawmakers who said they had been harassed or subjected to hostile and sexually suggestive comments by fellow members of Congress, some of whom are still in office. Shortly afterward, House Speaker Paul Ryan, R-Wis., sent a memo to fellow lawmakers encouraging them to complete sexual harassment training and make it mandatory for their staffs.

Last week, the Senate unanimously approved a measure requiring all senators, staff and interns to be trained on preventing sexual harassment.

On a voice vote, lawmakers adopted a bipartisan resolution calling for training within 60 days of the measure's passage.

Each Senate office would have to submit certification of completed training, and the certificate would be published on the public website of the secretary of the Senate.

The measure had widespread support, and the action occurred within days of the resolution's formal introduction.

Fox News' Jason Donner and The Associated Press contributed to this report.