On a conference call with campaign donors on Sunday evening, Mr. Buttigieg said he had reached the decision with regret but concluded it was “the right thing to do, when we looked at the math,” according to one person on the call. Without mentioning opponents by name, Mr. Buttigieg said he was concerned about the impact he would have on the race by staying in, saying Democrats needed to field “the right kind of nominee” against Mr. Trump.

Mr. Buttigieg talked with Mr. Biden and former President Barack Obama on Sunday night, according to a Democratic official familiar with the conversations. Mr. Biden asked for Mr. Buttigieg’s support and the former mayor indicated he would consider the request. Mr. Buttigieg wants to sleep on the decision, he told aides, some of whom believe he should move quickly to endorse Mr. Biden.

Mr. Obama did not specifically encourage Mr. Buttigieg to endorse Mr. Biden, said the official, who insisted on anonymity to discuss private conversations. But Mr. Obama did note that Mr. Buttigieg has considerable leverage at the moment and should think about how best to use it. Should Mr. Buttigieg endorse Mr. Biden on Monday, it could reshape the Democratic primary if many of his supporters shift to Mr. Biden, creating a more formidable centrist challenge to Mr. Sanders’s progressive movement.

In his remarks, Mr. Buttigieg directed criticism toward Mr. Sanders, without naming him, that he has previously made on the debate stage and on the campaign trail.