After nearly six hours of contract negotiations that stretched late into the evening, administrators at Community College of Philadelphia and union officials failed to reach an agreement Sunday but planned to continue talks at noon Monday. Classes at the 27,800-student school will be held Monday.

“While we have not yet made substantial progress on all of the outstanding issues on the table, we have decided to continue bargaining tomorrow afternoon in the hopes of making the progress necessary to avert a strike,” Junior Brainard, the union’s co-president, said in an email.

Negotiations have dragged on for three years, and union members last Wednesday overwhelmingly voted to authorize union leaders to call a strike.

The union, which represents 1,200 faculty and support staff, has not set a strike date but indicated a walkout could come as soon as this week. It could halt classes just weeks before the semester’s end and about a month before commencement.

“They feel they have no choice but to consider strike action,” said Randi Weingarten, president of the American Federation of Teachers, who attended a rally with union leaders at the college’s Spring Garden campus Friday. “The college really refuses to negotiate.”

College leaders remain adamant about their last offer. They say that they are prepared for a strike but hope to avoid one.

“There is always a possibility,” said Donald “Guy” Generals, college president. “As you know, we are pretty far apart.”

Generals said the college would try to hold classes if a strike occurred, but might have to suspend them if not enough professors showed up. College offices and buildings would remain open, he said.

Sunday’s meeting was the latest development in negotiations that have stalled, largely over issues of faculty workload, health insurance, and compensation.

Generals said in January that the college was considering imposing a contract on union members, its so-called last best offer, details of which were released in May. That proposal, retroactive to Sept. 1, 2016, and running through Aug. 31, 2021, would give union members more than a 10 percent cumulative raise, but also would require heavier workloads for newly hired faculty, as well as health-care contributions.

Union members have been operating under the terms of a contract that expired in August 2016.

Weingarten said a town hall meeting will be held this week to fully air the issues dividing the sides.

“We think it’s important to make sure the public knows the issues,” she said.