Stanford University and union negotiators met Tuesday to resume talks about retirement benefits under the existing labor contract, but no progress was reported by either side.

Service Employees International Union (SEIU), Local 715, called a one-day strike of both its university and hospital workers on Monday. The SEIU hospital contract has lapsed.

A federal mediator participated in Tuesday’s talks, said Zev Kvitky, spokesman for the university workers.

“We agreed to new negotiating sessions after the new year,” Kvitky said. “We are hoping to continue in good faith negotiations with Stanford.”

“We are committed to the negotiation process,” Alan Acosta, university spokesman, said. “We’re optimistic we can work out the issues on the table.”

SEIU represents about 1,300 university workers and about 1,400 workers at Stanford and Lucile Packard Children’s hospitals.

On Monday morning, 301 of 511 SEIU workers scheduled to work at the two hospitals showed up for work, a number that SEIU disputes. That meant that 58.9 percent of the workers on the morning shift crossed picket lines.

The number of university workers crossing picket lines was much lower. The university didn’t have exact figures, but Acosta said that only 10 percent of SEIU workers were on the job Monday. That includes all university departments and the Stanford Linear Accelerator Center.

— Don Kazak