WASHINGTON — Rep. John Conyers, D-Mich., the longest- serving member of Congress, stepped aside as the top Democrat on the House Judiciary Committee amid growing internal pressure as an ethics investigation begins into sexual harassment allegations.

Conyers, 88, said he would not resign from Congress and instead would fight the allegations in the hope of reclaiming his spot atop the committee overseeing federal laws and other legal issues. “I very much look forward to vindicating myself and my family before the House Committee on Ethics,” he wrote in a letter to House Minority Leader Nancy Pelosi, D-Calif., Sunday.

Conyers, 88, settled a sexual harassment allegation brought by a former staffer, leaving her on the payroll as a temporary employee and paying out just under $30,000.

Pelosi issued a statement immediately after Conyers’s announcement: “I particularly take any accusation of sexual harassment very seriously. Any credible accusation must be reviewed by the Ethics Committee expeditiously. We are at a watershed moment on this issue.”

The announcement came after days of internal pressure on Conyers, particularly from Pelosi, to step aside from the leadership post, according to a senior Democratic aide familiar with the process.

It followed a Sunday morning dominated by the sprawling issue of sexual harassment and assault on the political news shows. Initially, on NBC’s “Meet the Press,” Pelosi declined to say whether Conyers would suffer any immediate penalty over allegations that he sexually harassed a junior female aide in a case that was resolved with a payout to the ex-staffer.

“We are strengthened by due process. Just because someone is accused – and was it one accusation? Is it two? I think there has to be – John Conyers is an icon in our country,” Pelosi told NBC’s Chuck Todd, when asked whether the longest-serving member of the House should resign.

However, in a sign that she knew what was coming, Pelosi said she expected Conyers to take a step himself. “I believe he understands what is at stake here and he will do the right thing,” she said.

But members of Congress have said that the “due process” system is outdated and biased toward insulating the lawmaker from suffering penalties for misbehavior. “The whole system needs to have a comprehensive shift,” Rep. Jackie Speier, D-Calif., said on ABC’s “This Week.”

Speier and Rep. Barbara Comstock, R-Va., are the lead sponsors of legislation slated for a vote this week that would streamline the process, amid growing accusations about members of Congress that are similar to those involving powerful men from Hollywood, the media and Silicon Valley.

The legislation would require mandatory training on harassment and discrimination for all lawmakers, staff and interns who work in Congress. “There needs to be one standard for members,” Comstock said on “This Week,” noting that Con- yers benefited from making a payment that was never revealed until a BuzzFeed report last week, “No more secret payments.”

Conyers has denied any wrongdoing and said his payout was meant to resolve the issue and not constitute culpability.

His payout came from the regular allowance for lawmakers for staff salaries and other administrative costs. As The Washington Post reported this month, a separate account overseen by the Office of Compliance has paid out more than $15 million in settlements of sexual harassment and other cases of discrimination.

One Democrat, Rep. Kathleen Rice, N.Y., has suggested that Conyers should just resign from Congress altogether, something that Comstock voiced agreement for Sunday.