A stampede of Senate Democrats led by some of the party’s most endangered incumbents rushed forward on Tuesday calling for Senator Robert Menendez of New Jersey to resign, a day after he defiantly vowed to fight federal corruption charges and predicted he would be exonerated.

Even as Senator Chuck Schumer of New York, the majority leader, defended Mr. Menendez as a “dedicated public servant” and refused to publicly move to push him out, the drumbeat for Mr. Menendez to step down grew from within his ranks. That left Mr. Schumer in a difficult position, caught between his role as the leader and defender of all Senate Democrats and the political imperative of cutting loose a member of his caucus who had become a political liability in an already difficult slog to keep the party’s Senate majority.

The most notable call for Mr. Menendez to go came from Senator Cory Booker, the junior senator from New Jersey who has long been a close friend and fierce defender of Mr. Menendez. Mr. Booker, who testified as a character witness for Mr. Menendez during his first corruption trial, said the “shocking allegations of corruption” were “hard to reconcile with the person I know.”

He added: “I believe stepping down is best for those Senator Menendez has spent his life serving.”

His call came amid a flood of calls by Democrats running for re-election next year in politically competitive states, who appeared eager to distance themselves from Mr. Menendez. The third-term senator was indicted last week on bribery charges in what prosecutors alleged was a sordid scheme that included abusing his power as chairman of the Senate Foreign Relations Committee to benefit Egypt.

Senator Jon Tester of Montana, who is running in a state that former President Donald J. Trump won by more than 16 points in 2020, said Mr. Menendez needed to go “for the sake of the public’s faith in the U.S. Senate.” Senator Sherrod Brown of Ohio, a onetime bellwether state that has shifted sharply to the right over the past two presidential election cycles, said Mr. Menendez had “broken the public trust and should resign from the U.S. Senate.”

And Senator Jacky Rosen of Nevada, who launched her re-election bid in a battleground state by predicting that her race would decide control of the Senate, said the corruption charges were a “distraction that undermines the bipartisan work we need to do in the Senate for the American people.”

Democrats view the fact that they were able to get all of their vulnerable senators to run for re-election in 2024 as their biggest source of strength in their quest to hold onto their slim majority next year.

By noon, those vulnerable Democrats had helped open the floodgates, with more than a dozen Democratic senators from across the country joining them and rushing to release statements calling for Mr. Menendez’s resignation ahead of their weekly lunch in the Capitol. “No one is entitled to serve in the U.S. Senate, and he should step aside,” said Senator Michael Bennet of Colorado.

“That’s a breach of that trust and a burden I believe will prevent him from fully serving,” said Senator Mark Kelly of Arizona. “He should resign.”

Senator Kirsten Gillibrand of New York said later in the afternoon that she agreed with Mr. Booker that Mr. Menendez should step down.

As New Jersey’s junior senator, Mr. Booker often has described Mr. Menendez, the senior senator, as a friend, ally and mentor. But the nature of the charges — along with the political landscape of the state — appeared to have played a role in changing his mind.

Even before the latest indictment was announced, opinion polls indicated that public support for Mr. Menendez was waning, said Patrick Murray, director of the Polling Institute at Monmouth University in New Jersey.

During Mr. Menendez’s first criminal indictment, “New Jersey voters, and particularly Democrats, were willing to give him the benefit of the doubt,” Mr. Murray said. “This time, public opinion is different.”

In the Senate, it took Democrats days to get around to condemning their colleague.

On Friday, Mr. Menendez stepped down temporarily as chairman of the Foreign Relations Committee, under the rules put in place by his own party, but Mr. Schumer defended his right to remain in office. Karine Jean-Pierre, the White House press secretary, said any decision about Mr. Menendez’s future in the Senate was “going to be up to him and the Senate leadership.”

A lone Democratic voice over the weekend adding to calls for Mr. Menendez to go was Senator John Fetterman of Pennsylvania, who hails from another battleground state. He vowed to return campaign donations from Mr. Menendez’s leadership PAC in envelopes stuffed with $100 bills — an apparent reference to the indictment against Mr. Menendez, which said investigators found jackets and envelopes stuffed with cash at his home, allegedly containing the fruits of the senator’s corrupt dealings.

Mr. Fetterman, who has come under criticism from his colleagues for pressing for a dress code change in the fusty Senate to accommodate his shorts-and-hoodie uniform, on Tuesday said he hoped his Democratic colleagues would “fully address the alleged systematic corruption of Senator Menendez with the same vigor and velocity they brought to concerns about our dress code.”

Representative Nancy Pelosi, the former House speaker from California, on Monday night also weighed in on the Menendez scandal, helping wedge open the door for detractors, saying on MSNBC that it would “probably be a good idea” for him to resign.

Some Republicans, on the other hand, jumped to Mr. Menendez’s defense, arguing that Democrats should have to weather the political consequences of his conduct.

“He should be judged by jurors and New Jersey’s voters, not by Democratic politicians who now view him as inconvenient to their hold on power,” Senator Tom Cotton, Republican of Arkansas, wrote on X, previously Twitter.

Speaker Kevin McCarthy, however, said on Saturday that Mr. Menendez should go, arguing that the case laid out by prosecutors was “pretty black and white.” In contrast, Mr. McCarthy, a California Republican, has defended one of his own indicted members, Representative George Santos of New York, saying that it was not up to him to decide whether he should represent his district.

“You know why I’m standing by him? Because his constituents voted for him,” Mr. McCarthy said of Mr. Santos in January.

Mr. Menendez won re-election in 2018 by a 12-point margin.

Christopher Maag contributed reporting from New York.