House Minority Leader Nancy Pelosi struggled to answer questions Sunday about harassment allegations against Rep. John Conyers Jr. (D-Mi.) (Marvin Joseph/The Washington Post)

Congressional leaders are under increasing pressure to respond swiftly to sexual misconduct allegations involving prominent members, following an outcry from female lawmakers who believe their male colleagues are being treated more gently than offenders in the private sector.

“If you look, the media and corporate America has been firing people,” Rep. Barbara Comstock (R-Va.) said Sunday on ABC’s “This Week,” noting the swift dismissal by CBS and PBS of Charlie Rose after The Washington Post’s report of harassment allegations. “We have to have the same kind of standards.”

In recent days, both parties have faced allegations against prominent male members, with ethics inquiries into harassment opened against Rep. John Con­yers Jr. (D-Mich.) and Sen. Al Franken (D-Minn.). The political future of Rep. Joe Barton (R-Tex.) was thrown into question when nude photos of the congressman surfaced on social media, and a former girlfriend said he had threatened to report her to the Capitol Police if she exposed his behavior.

The first sign of intensifying pressure on leadership came Sunday, when Conyers, the longest-serving member of Congress, stepped aside as the top Democrat on the House Judiciary Committee.

Behind the scenes, House Minority Leader Nancy Pelosi (D-Calif.) had tried to guide Conyers to give up the leadership post, according to a senior Democratic aide familiar with the process. Conyers’s resistance to the effort was backed by some members of the Congressional Black Caucus, which Conyers co-founded more than 45 years ago.

Several lawmakers called for changes to the way Congress handles allegations of sexual misconduct after two prominent democrats were accused of impropriety. They also, however, stressed due process resisting immediate calls for resignations. (Meg Kelly/The Washington Post)

On Sunday, Pelosi appeared on NBC’s “Meet the Press” and struggled to handle questions about Conyers, 88, a onetime civil rights leader.

At first, Pelosi, the first female House speaker, stressed that he needed to have “due process” and called Conyers “an icon of history.” Then she hinted that eventually Conyers would “do the right thing.”

By lunchtime, Conyers announced he would step down from the committee post. “I very much look forward to vindicating myself and my family before the House Committee on Ethics,” he wrote in a statement that Pelosi’s advisers circulated to the media.

Some female members had demanded that Conyers resign his seat. Rep. Kathleen Rice (D-N.Y.), who last week called for him to step down, told CNN on Friday that voters are “sick and tired of the rules in Washington” being different from those for the rest of the country.

Rep. Jackie Speier (D-Calif.), who is leading a fight for tougher penalties against lawmakers, stopped short of demanding that Conyers resign in her Sunday appearance on “This Week.” But she joined her colleagues in criticizing the ethics committee process as too slow in handling most investigations.

She advocated that the panel receive more funding so it could “move very swiftly, not wait years,” to investigate the Conyers allegations.

Speier said there needed to be an entire shift in culture, from the bottom up, that would make it easier for victims to come forward and would end the process of allowing lawmakers to use taxpayer funds to secretly settle these cases.

“We say zero tolerance, but I don’t believe that we put our money where our mouths are,” she said.

This week, the House is scheduled to vote on a measure sponsored by Speier and Comstock that would require mandatory training on harassment and discrimination for all lawmakers, staff and interns who work in Congress.

Many staffers have said they have no idea how to file complaints, and those that have gone through that process have described it as cumbersome. Comstock said she and Speier were just beginning their work on the issue, promising further action after this first bill passes.

In particular, she singled out how Conyers settled a sexual harassment complaint brought by a former staffer in 2015, leaving the woman on the payroll as a temporary employee and paying out just under $30,000. That payout came from the lawmaker’s regular allowance for staff salaries and other administrative costs, different from a separate account overseen by the Office of Compliance, which has paid out more than $15 million in settlements of sexual harassment cases and other instances of discrimination.

“No more secret payments,” Comstock said.

After more than a week in seclusion, Franken gave his first interviews to his home-state media, defending himself against allegations that he inappropriately groped or forcibly kissed four women. The Senate’s ethics panel is investigating.

Franken pledged to return to the Capitol on Monday in a bid to win over his state’s voters, declining to resign after allegations that he groped several women in photo opportunities and that he forcibly kissed an entertainer while on a USO tour in 2006 before he was a senator.

“I’m embarrassed and ashamed. I’ve let a lot of people down and I’m hoping I can make it up to them and gradually regain their trust,” Franken told the Star Tribune, his first interview since the allegations emerged Nov. 16.

He denied that he intentionally grabbed women’s backsides during photos, saying that he did not remember the particular pictures in question.

Pelosi also suggested that the Franken case was partly different because one of his alleged victims has publicly accepted his apology — in contrast to women in Alabama who have said Republican Senate candidate Roy Moore tried to have improper relationships with them when they were teenagers and he was in his 30s, working as a local prosecutor.

“I don’t think that you can equate Senator Franken with Roy Moore. It’s two different things,” the Democratic leader said.

The allegations against Barton involved consensual behavior. He apologized last week after a nude picture of him appeared on social media, part of what The Washington Post later reported was a years-long relationship with a woman who confronted him over his other relationships with women he met online. Barton has not discussed the allegations.

Barton, 68, has until Dec. 11 to file for reelection in Texas’s 6th Congressional District, which includes his home town, Ennis, and portions of the cities of Arlington and Fort Worth. As of Sunday, the only candidate listed on the Texas secretary of state’s website was the Democrat whom Barton defeated by nearly 20 percentage points last year.

Last week Barton told the Texas Tribune he was still deliberating whether to run for another term.