“I would hope governors listen to the public health experts and what they are saying is, you just indicated, we don’t want gatherings of more than 50 people,” Mr. Sanders said. “I’m thinking about some of the elderly people sitting behind the desks, registering people, all that stuff. It does not make a lot of sense. I’m not sure that it does.”

The four states that are scheduled to hold primaries on Tuesday issued a joint statement on Friday expressing confidence that ballots could be safely cast and reconfirmed their plans on Saturday.

On Sunday night, after the new recommendations from the C.D.C., a spokesman from the Illinois secretary of state’s office said that “as of now, we are still on for Tuesday.”

“We’ve now had 38 days of early voting and hundreds of thousands of vote-by-mail ballots have been issued,” said the spokesman, Matt Dietrich. “We continue to encourage voters to help mitigate Election Day traffic by early voting on Monday.”

He added that “voters are urged to maintain proper distance between themselves and other voters.”

In New York, Mr. Kellner, the elections board co-chair and a Manhattan lawyer, said he was in favor of moving the election to June 23 — the day of another already scheduled statewide vote.

“Why? There’s no compelling reason to have the presidential primary election in April apart from the other election,” Mr. Kellner said. He added that it was likely that the presumptive Democratic presidential nominee would be decided by late April and, if not, the June 23 election date still fell before the Democratic National Convention in Milwaukee in July.

Many officials do not regard a postponement as immediately necessary, Mr. Kellner said, adding that a decision could be delayed for two weeks, when more information will be available.