The Chicago Teachers Union and city officials returned to the bargaining table Monday afternoon, hours after the union rejected a sweetened contract offer that would increase teacher salaries 16% over five years.

In rejecting the offer, the union started a 30-day clock for a potential strike by dismissing an independent fact-finder’s report that was made public Monday.

Mayor Lori Lightfoot had announced the $351 million contract offer based on the report of the fact-finder, who met with both the district and teachers union last month in an effort to help resolved the dispute.

“There’s no reason a deal can’t be reached by the start of the school year,” Lightfoot said Monday at a press conference at Webster Elementary School on the West Side. “There’s no reason there should be a strike. We have 30 days to get the job done. We could get this done today. We’ve put, I think, a very robust offer on the table.”

Though a deal before the first day of school next Tuesday seems unlikely, Lightfoot wants to avoid a teachers strike similar to the one in 2012 that marred the start of former Mayor Rahm Emanuel’s tenure and his relationship with the city’s teachers thereafter.

But CTU leaders said the fact-finder ignored many of its concerns about staffing and wraparound support for students.

“The fact-finder’s report was silent on a number of our key concerns that addressed conditions in our schools and classrooms,” CTU President Jesse Sharkey said at a union news conference outside Suder Montessori Magnet Elementary School, also on the West Side.

“Though the wage and benefit proposals will be said to be generous by the mayor and CPS’ team, they come in the context of nearly a decade of austerity and cuts for Chicago’s teachers and other school staff,” Sharkey said. “We’ve endured three freezes, multiple furloughs, layoffs and other cuts.”

Despite the mayor’s proposal on wages, Lightfoot has refused to include in a contract the union’s demands for librarians and nurses at every school, more special education and bilingual support, smaller classes and a counselor for every 250 students. She has instead vowed to accede to some of those demands outside of the CTU contract.

“The contract does not represent the full scope of important issues that we are committed to addressing with our teachers, school leaders and families,” CPS CEO Janice Jackson said. “It is well known that the teachers union has prioritized issues that the fact finder concluded fall outside of bargaining. These are matters where we share mutual interests.”

Sharkey said some progress has been made at the bargaining table, though the two sides remain a “really, really, really long way away” from a deal. He said four main issues — staffing shortages, pay and benefits, class sizes, and more nurses and counselors — are the main sticking points for the CTU.

“This union is going to continue preparing for a strike, if need be, in order to deliver those improvements for our members and for the people who rely on public schools in the city of Chicago,” Sharkey said.

While the fact-finder made no recommendations on many of those key issues, he sided with CPS in recommending a five-year deal. The report’s suggestion on wages and employee health contributions was a compromise between the two sides’ proposals, with the fact-finder recommending a 16% raise over five years instead of CPS’ proposed 14% raise over that term. The teachers union had asked for a 15% raise over three years.

Employee contributions to health care, meanwhile, should go up by 1% over the last three years of a five-year deal, the fact-finder’s report said. CPS had proposed raising employee contributions to health care by 1.5% over that time, while the CTU asked to maintain current contributions.

The CTU had originally proposed a three-year, $3 billion contract with that 15% pay raise in a deal that would “rebuild” the city’s public school system with wraparound services that would support students faced with trauma.

The fact-finder’s report was given to both sides on Aug. 8 and publicly released Monday. With the report’s rejection, the CTU now can vote at any time to authorize a strike. Illinois law requires the union wait 30 days after the rejection of the report before enacting a work stoppage, meaning the earliest the CTU can strike is Sept. 25.

Teachers likely would not walk out until October, however, because they temporarily lose their health coverage if they aren’t working at the start of the month. Indications from the CTU point to a mid-September authorization vote at the earliest.