In a letter to the board on Sunday, Mr. Sanders’s campaign had urged the board to keep him on the ballot and hold a primary in the interest of party unity. On Monday, the Sanders-aligned group Our Revolution said they would challenge the decision.

“We will not stand by and allow New York Democrats to be denied the opportunity to influence their party and its platform at the convention in August,” the group’s chair, Larry Cohen, said in a statement on Monday. “We will be forced to go to the credentials committee and challenge any delegates that New York sends to the convention.”

With the decision, made during a telephone meeting by the two Democrats on the election board, New York became the first state to cancel its presidential primary, only the latest major development in the shifting national electoral landscape. In response to the coronavirus epidemic, 16 states have postponed their primaries and many have taken measures to encourage voting by mail.

Despite arrangements to encourage absentee voting, polling places are expected to remain open in about 42 counties for down-ballot races.

Andrew J. Spano, the other board member who voted in the unanimous decision, said the chance a primary could spread coronavirus to both the public and poll workers counterbalanced the wishes of Mr. Sanders’s supporters.

Mr. Spano, a former Westchester County executive, said he had only reached a conclusion on how to vote on Monday morning, following what he described as a roller coaster weekend, but ultimately concluded, “We should minimize the risk.”

Asked about the decision at his daily coronavirus briefing in Albany, Gov. Andrew M. Cuomo said he would not “second guess” the board and cited the safety of election employees. Later, in a radio interview, Mr. Cuomo reiterated that it was the board’s decision, but wondered why Mr. Sanders would still want a full primary.