CHICAGO — Chicago teachers have voted to authorize their union leaders to call a strike, setting the stage for a possible work stoppage next month in the nation’s third-largest school district, officials announced Thursday.

Chicago Teachers Union delegates are set to meet next week to set a deadline for a strike, though the earliest one could happen is Oct. 7.

The union and the school district have been negotiating for months over issues including pay, benefits and staffing shortages. The union argues that years of budget cuts have shortchanged schools, resulting in overcrowded classrooms and far fewer nurses and librarians.

After three days of voting, union leaders announced that 94 percent of the votes counted backed giving leaders the authority to call a strike.

“Our school communities are desperately short of nurses, social workers, psychologists, counselors and other support staff, even as our students struggle with high levels of trauma driven by poverty and neighborhood violence,” CTU president Jesse Sharkey said in a statement. “This vote represents a true mandate for change.”

Officials with Chicago Public Schools say the district has made improvements in recent years, thanks in part to additional revenue from a property tax hike and the state’s revamped school funding formula. They say they’ve offered general salary raises, but the union disagrees.

The union, which represents roughly 24,000 educators, wants a 15 percent total raise over a three-year contract. The district has offered a 16 percent total raise over a five-year contract. Other issues include class size, sanctuary protections for students and elementary school prep time.

Chicago’s last major teachers strike was in 2012 and it lasted seven school days. But the tone and issues are far different this time. The mayor then, Rahm Emanuel, had a more contentious relationship with the union than the current mayor, Lori Lightfoot, and the district’s finances were shakier.

The contract dispute is one of Lightfoot’s first major tests as mayor, as she took office earlier this year.

Earlier on Thursday, Lightfoot said representatives should be negotiating 24 hours a day, seven days a week to get a deal.

“Having a strike would be catastrophic for the learning environment for our kids,” Lightfoot said.

After the strike vote was announced, Lightfoot issued a statement saying that the city remained committed to reaching a negotiated settlement.

Other school employee unions, including custodians and bus drivers, are also in contract fights that could lead to simultaneous strikes.

Roughly 400,000 students attend district schools.