Top House Democrats -- including Minority Leader Nancy Pelosi and members of the Congressional Black Caucus (CBC) -- are pressuring Rep. John Conyers, D-Michigan, to step down, two senior Democratic aides confirmed to CBS News.

Conyers, 88, is facing a congressional investigation into sexual harassment allegations. He said he would step aside as the ranking member on the House Judiciary Committee as a result.

U.S. Rep. John Conyers were spotted on a plane on Nov. 28, 2017. Courtesy of Dennis Lennox

The Detroit Free Press reported that a Republican consultant and pundit, Dennis Lennox, tweeted a photo of Conyers on a flight to Michigan on Tuesday. Conyers missed two roll call votes on Tuesday.

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CBC chairman Cedric L. Richmond (D-La.) released a statement late Tuesday after meeting with Conyers earlier in the day.

"Today I met with John and we had a very candid conversation about the seriousness of the allegations against him, which he vehemently denies," Richmond's statement read. "I told him that I agreed with his decision to step down as ranking member of the House Judiciary Committee at this time. I also told him that I encourage and expect him to fully cooperate with the ethics investigation. He said he would."

Richmond said in the statement that any decision Conyers "to resign from office before the ethics investigation is complete is John's decision to make."

The CBC was established in 1971 and has a historic 49 members for the 115th Congress. Richmond's statement mentions that the CBC supports mandatory sexual harassment training for members and staff, as well as proposed changes to the sexual harassment complaint process in Congress.

CBC will hold sexual harassment training for its members this week, according to the statement.

"The Congressional Black Caucus calls on Congress to treat all members who have been accused of sexual harassment, sexual assault, and other crimes with parity," the statement read. "We call on Congress and the public to afford members with due process as these very serious allegations are investigated."

Conyers was first elected in 1964, The Associated Press reports, and was one of the founding members of the CBC. Conyers is the longest-serving current House member.

Rep. Bennie Thompson (D-Miss.) said he met with Conyers on Tuesday to say he was concerned for him.

"I think he should go home and talk to his constituents and listen to them and make a decision based on that," Thompson said.

Also Tuesday, the House's top Democrat wrote a letter to the House Ethics Committee urging them to move quickly with its inquiry.

"We are at a watershed moment for our country in the fight against sexual harassment and discrimination," Minority Leader Nancy Pelosi (D-Calif.) said. "The Committee on Ethics has a great responsibility to proceed expeditiously as well as fairly into any investigation of credible harassment and discrimination allegations."

The development comes after BuzzFeed News reported that Conyers' office paid a former staffer more than $27,000 to settle a complaint. That staffer said she was fired for rejecting his sexual advances, according to the report.

BuzzFeed also reported that another woman who worked for Conyers said she faced "daily" harassment, in a lawsuit she abandoned when the court denied her request to keep it sealed. In that lawsuit, BuzzFeed reported, the woman also said Conyers' wife, Monica Conyers, accused the woman of wanting to have an affair with her husband.

Conyers said the allegations were "raised by documents reportedly paid for by a partisan alt-right blogger" and looks "forward to vindicating myself and my family before the House Committee on Ethics."

Meanwhile, a former deputy chief of staff said Conyers made an unwanted sexual advance toward her and touched her inappropriately twice in the late 1990s.

Deanna Maher, 77, who ran a Michigan office for Conyers from 1997 to 2005, told The Detroit News that there were three instances of inappropriate conduct.

She says the first was in 1997, when she rejected his offer to share a hotel room and have sex.

The others involved unwanted touching in a car in 1998 and unwanted touching of her legs under her dress in 1999.

Maher said the first instance of harassment happened shortly after Conyers hired her in 1997 during an event with the Congressional Black Caucus in Washington.

"I didn't have a room and he had me put in his hotel suite," said Maher, adding that she rejected his offer to share his room at the Grand Hyatt in Washington and have sex.

Conyers' attorney Arnold Reed told the newspaper that he questioned why Maher would work for Conyers for so many years after the alleged allegations. He said her allegations are uncorroborated and Conyers denies wrongdoing.

"He maintains that he has not done anything wrong," Reed said.

Last week, Melanie Sloan, a high-profile Washington lawyer, said Conyers verbally abused her repeatedly when she worked for him.

Sloan says while she was not sexually harassed when she worked for Conyers, he would often berate her and criticize her appearance, reported CBS News' Nancy Cordes. She said his actions went beyond being just a tough boss.

"He screamed at me in front of a bunch of domestic violence advocates," Sloan said.

Sloan worked for Conyers from 1995 to 1998 as a House Judiciary Committee staffer. Sloan said Conyers was constantly verbally abusive.

"He would yell and scream at me. There was a time where he screamed at me for not wearing stockings," she said.

CBS News' Catherine Reynolds and Emily Tillet contributed to this report.