Representatives of both Mr. Sanders and Mrs. Clinton moved quickly to try to quell the furor on Tuesday. Fresh off recent battles with not only Ms. Warren but also former Vice President Joseph R. Biden Jr., Mr. Sanders’s campaign was eager to avoid another fight that would distract from his closing message less than two weeks before the Iowa presidential caucuses. Mr. Sanders apologized on Monday to Mr. Biden after a Sanders campaign surrogate wrote an opinion article accusing the former vice president of having “a big corruption problem.”

Speaking to reporters on Tuesday in Washington, Mr. Sanders said: “Secretary Clinton is entitled to her point of view. My job today is to focus on the impeachment trial.”

When asked for his response to Mrs. Clinton’s assertion that no one liked him, he joked that “on a good day, my wife likes me, so let’s clear the air on that one.”

Mrs. Clinton tried to clarify her remarks on Tuesday evening. “I thought everyone wanted my authentic, unvarnished views!” she wrote on Twitter. “But to be serious, the number one priority for our country and world is retiring Trump, and, as I always have, I will do whatever I can to support our nominee.”

Those who have spoken to Mrs. Clinton recently confirm that she has every intention of supporting the Democratic nominee — even if Mr. Sanders ends up winning the primary. Still, even some longtime allies were shocked that she voiced such criticisms of Mr. Sanders in an election year, so close to the start of primary voting.

They were far less surprised by the content of her remarks.

Mr. Sanders’s denial in his dispute with Ms. Warren over whether he had told her a woman could not defeat Mr. Trump infuriated Mrs. Clinton, according to people close to her. Mr. Sanders’s subsequent refusal to chastise his supporters for attacking Ms. Warren and her team online only added to her concern.

“It’s not only him, it’s the culture around him. It’s his leadership team. It’s his prominent supporters. It’s his online Bernie Bros,” Mrs. Clinton told The Reporter. “It should be worrisome that he has permitted this culture — not only permitted, seems to really be very much supporting it.”