LOS ANGELES (Reuters) - Tens of thousands of striking Los Angeles teachers were joined by parents and students in a rally near City Hall on Friday, as contract talks mediated by the mayor resumed behind closed doors after a marathon negotiating session the day before.

Some 30,000 teachers walked off the job on Monday in their first strike against the Los Angeles Unified School District (LAUSD) in 30 years, demanding higher pay, smaller classes and more support staff.

LAUSD officials have argued that the teachers’ demands would place too great a strain on the district’s budget if they were fully met. Union leaders have countered that sufficient funding is available if the district had the right priorities.

“We are willing to go as long as it takes and work as hard as we need to get a fair contract,” union bargaining chair Arlene Inouye told supporters at City Hall, adding that talks were expected to last through the three-day holiday weekend.

School district Superintendent Austin Beutner said later he was committed to reaching a deal in time to bring teachers back to school on Tuesday. But he added, “We have to solve it, unfortunately, with the resources that we have.”

The nation’s second-largest school district has kept its 1,200 campuses open with administrators and substitute teachers, but only a fraction of the 500,000 affected students have turned up, mostly gathered in gymnasiums and assembly halls.

At the urging of Mayor Eric Garcetti, negotiators for the United Teachers Los Angeles union and the district returned to the bargaining table on Thursday for the first time since talks broke off a week ago.

FILE PHOTO: Los Angeles teachers carry signs as they picket in the rain in Los Angeles, California, U.S. January 16, 2018. REUTERS/Dan Whitcomb

Garcetti, who lacks direct authority over the school district but is mediating the talks, said in a statement that the two sides had a “productive day of contract negotiations” on Thursday that ran past midnight.

Negotiators were back at it on Friday but offered no further clues about their progress after agreeing to a news blackout.

Seeking to strengthen its position at the bargaining table, the union staged a boisterous mass rally near City Hall, where tens of thousands of teachers, parents and students in red T-shirts filled a downtown park and surrounding streets.

“You can see how serious we are here. We’re not backing down,” said Richard Peterson, 65, a teacher at Northing Middle School in the city’s San Fernando Valley.

The job action follows a wave of teacher strikes last year across the United States over salaries and school funding, including walkouts in West Virginia, Oklahoma and Arizona. But the Los Angeles work stoppage differs in that educators face a predominantly Democratic political establishment more sympathetic to their cause.

Several possible contenders for the 2020 Democratic presidential nomination, Garcetti among them, have voiced solidarity with the strike. Support also was running high among parents and the public at large as reflected in a recent survey of Los Angeles residents.

Beutner told a news conference Friday evening the strike had already cost the district about $125 million - education funding in California is based on daily attendance - and collectively cost students more than 1.5 million days of instruction.

He said giving the teachers all they demand would ultimately require greater investment in education at the state level.

On Thursday, UTLA President Alex Caputo-Pearl said disgreements over proposals to reduce class size pose the biggest stumbling block to a settlement.

Another major point of contention has been the union’s call for curbing the steady expansion of independently managed charter schools, arguing that they divert resources from traditional classroom instruction.