Public school students in Chicago woke up Monday facing another day of canceled classes, as a labor stalemate continued between the city and its teachers’ union over in-person instruction and pandemic safety.

Hundreds of thousands of students in Chicago’s school district, the third largest in the country, have not attended school since classes were dismissed last Tuesday, because members of the Chicago Teachers Union voted to stop reporting to work amid concerns over the rapidly spreading Omicron variant. On Sunday night, the city announced that classes would not be held again Monday.The union, citing concern for the safety of its teachers, has insisted that the city switch temporarily to virtual learning.

“Honestly, remote learning is an important tool. We’ve learned a lot about what to do and not to do around it,” Jesse Sharkey, the union president, said at a news conference on Saturday. He acknowledged that remote learning was not as effective as in-person schooling. “But we’re dealing with the high point of a surge, and we have to have adequate safety measures in place.”

Under a proposal that the union outlined on Saturday, teachers would have distributed equipment and materials for online instruction and helped parents sign up for virus testing on Monday and Tuesday, and then taught students remotely for the rest of the week.

At a news briefing on Monday, Jen Psaki, the White House press secretary, said that President Biden believes that schools “should be open across the country,” adding that the president was in touch with Mayor Lori Lightfoot of Chicago and Gov. J.B. Pritzker of Illinois.

“The mental health impact on kids of not having schools open is very harsh and hard, and he does not want to see schools closed across the country,” Ms. Psaki said. “There’s no secret about that. That continues to be what he states.”

City officials have repeatedly rejected remote learning as an option. But on Sunday morning on the NBC program “Meet the Press,” Mayor Lightfoot said her team spent Saturday evening drafting a new proposal to give to the union. Classes would still be in-person, but the new proposal, the mayor said, had a list of conditions that could trigger a switch to virtual learning on a school-by-school basis.

Although both sides reported on Sunday night that they were still negotiating, the parties exhibited some of the animosity that has characterized the talks.

On “Meet the Press,” Ms. Lightfoot condemned the union for “being critical and throwing bombs.” And she described the union’s vote last week to stop reporting to work as an illegal walkout. “They abandoned their post, and they abandoned kids and their families,” Ms. Lightfoot said.

In a statement on Sunday, the union said that “educators are not the enemy Mayor Lightfoot wants them to be. They are parents, grandparents, clergy, community partners and Chicagoans.”