House Minority Leader Nancy Pelosi and Speaker Paul Ryan said Thursday that Rep. John Conyers should resign from Congress as he faces a series of sexual misconduct and harassment allegations.

"The allegations against Congressman Conyers, as we have learned more since Sunday, are serious, disappointing and very credible. It's very sad. The brave women who came forward are owed justice. I pray for Congressman Conyers and his family and wish them well, however, Congressman Conyers should resign.," said Pelosi, a California Democrat, at her weekly press conference.

Speaker Ryan, R-Wisconsin, echoed that message at his weekly press conference afterward: "Yes, I think he should resign. He should resign immediately."

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Other members of House Democratic leadership have called on Conyers to resign including Reps. Steny Hoyer, D-Maryland, Rep. Jim Clyburn, D-South Carolina and Rep. Joe Crowley, D-New York. Rank and file members calling him to resign including Reps. Kathleen Rice, D-New York, Earl Blumenauer, D-Oregon, David Cicilline, D-Rhode Island and Pramila Jayapal, D-Washington.

Their comments came as Conyers is in a Detroit hospital for a stress-related illness, CBS News confirmed earlier in the morning.

Conyers' lawyer, Arnold Reed, told reporters Thursday that the 88-year-old Michigan Democrat suffered shortness of breath, chest pains, lightheadedness and dizziness while he was walking around his home Wednesday night. He also lashed out against Pelosi over her call for Conyers' resignation.

"Nancy Pelosi did not elect the congressman, and she sure as hell won't be the one to tell the congressman to leave," Reed said during his press conference in Detroit.

"He is not going to be pressured by Nancy Pelosi or anyone else to step down," Reed said.

Multiple women have accused Conyers of sexually harassment and trying to cover up the accusations.

Two senior Democratic aides confirmed to CBS News on Tuesday that Pelosi and members of the Congressional Black Caucus (CDC) were pressuring Conyers to resign.

Conyers' lawyer told the Associated Press Wednesday he has no plans to resign. He did step down as ranking member of the House Judiciary Committee last weekend.

Buzzfeed was the first news outlet to report last week about a settlement Conyers made with a former staffer who had accused him of sexual misconduct. Conyers eventually acknowledged the settlement, but denied wrongdoing. Another former staff member accused Conyers of sexual misconduct and filed a lawsuit, but dropped the suit when the court refused to seal the case.

CBS News' Kathryn Watson, Emily Tillett and Blair Guild contributed to this report.