Senator Fetterman is hoping to sideline Senator Menendez in the Senate over his alleged crimes while efforts to censure other members of Congress amass in the lower chamber.

Mr. Fetterman on Thursday introduced a measure that would strip Mr. Menendez as well as any other senator indicted on charges of mishandling classified information, acting as a foreign agent, or compromising national security of their committee assignments and their ability to access classified information.

“The Senate has an obligation to its constituents and this country to do everything it can to protect national security, and that means making sure that senators who are currently indicted for acting as agents of foreign powers don’t have access to our most sensitive national secrets,” Mr. Fetterman said in a statement.

He added that if “an indicted senator doesn’t have the guts or basic decency to step down, the Senate must act to protect national security and the institution itself.”

Mr. Menendez was indicted last month on charges of corruption and bribery, with federal prosecutors accusing him of leveraging his position in the Senate to benefit Egypt and help his wife’s friend to maintain the import monopoly of a New Jersey-based halal foods exporter in Egypt.

In the indictment, prosecutors disclosed that they had found gold bars and cash stuffed in jacket pockets at the New Jersey senator’s home.

Mr. Fetterman, a freshman senator, has been the loudest voice in the upper chamber in calling on his colleague to step down. Leadership has so far been reluctant to call for Mr. Menendez’s resignation.

Last month, Mr. Fetterman spearheaded an effort to expel Mr. Menendez from the legislative body after a superseding indictment added charges to the original indictment.

Mr. Fetterman’s push in the Senate comes alongside a week of drama in the House, which saw feuding members introduce resolutions to censure and expel each other from the body.

A measure introduced by Congresswoman Marjorie Taylor Green aimed at censuring Congresswoman Rashida Tlaib for what Ms. Greene called “antisemitic activity, sympathizing with terrorist organizations, and leading an insurrection at the U.S. Capitol complex” failed on Thursday.

The House voted to table Ms. Greene’s effort Wednesday, and, subsequently, a resolution aimed at censuring Ms. Greene was introduced by Congresswoman Becca Balint.

Ms. Balint’s resolution was aimed at censuring Ms. Greene for fanning “the flames of racism, antisemitism, hate speech against the LGBTQ community, Islamophobia, Asian hate, xenophobia, and other forms of hatred.”

President Biden’s son, Hunter Biden, had previously called on the House to censure Ms. Greene after she displayed obscene photos of him with escorts during a televised hearing and accused him of sex trafficking.

While Ms. Balint pulled her resolution against Ms. Greene before it was voted on, 23 Republicans joined with Democrats to vote against censuring Ms. Tlaib, some of them citing issues they had with the language of the resolution.

“I don’t think that Congresswoman Tlaib was violent. I don’t think that she was trying to overthrow a government,” Congressman Richard McCormick said in a social media post.

Also this week, the House considered a motion to expel Congressman George Santos from Congress; it ended up being the second failed effort to expel Mr. Santos this year.

The Republican-led effort ran aground in part because the House Committee on Ethics has an ongoing investigation into Mr. Santos, though it’s not clear if the body will vote on his expulsion again after the investigation is completed.

In an interview with Fox News, Speaker Johnson appeared unfazed by the drama playing out in the House, telling the network that the issues were “resolved on the floor.”

“You know, there is a view here that if you go down that road and you begin to censor one another, you kind of open a Pandora’s box,” Mr. Johnson said. “A lot of members of Congress say a lot of really foolish things.”