Ontario's Minister of Labour Kevin Flynn is hoping two of Canada’s largest universities will return to the bargaining table after the unions representing the schools' striking teaching assistants walked off the job this week.

Flynn says provincial mediators working with both York University and the University of Toronto are hopeful deals can be negotiated to bring a quick end to the strikes.

"Negotiations are obviously tough by nature, but we’re hoping that if we get cooler heads to prevail that all the issues can be sorted out at the table," he told The Canadian Press on Tuesday.

Earlier in the day, York University's 3,700 TAs and contract faulty hit the picket line, following CUPE Local 3903's rejection of the school’s tentative agreement Monday night. They joined the already-striking U of T workers.

At issue for the union representing York workers are wages and job security for contract employees, as well as rising tuition fees and student debt, said union representative Faiz Ahmed.

"We are looking for job security for teachers who teach on a term-by-term basis," Ahmed told reporters outside York University's Keele Street entrance.

Of particular concern is a funding package for TAs worth $16,000 per year, which they say leaves them living below the poverty line.

On Monday night, York University president Mamdouh Shoukri issued a statement to acknowledge the concerns of students and their parents.

"I share their concerns," Shoukri said. "I am confident that, when we return to the bargaining table, we will reach a fair and competitive settlement…"

One female York student said she supports the strike if it means a better deal for TAs and contract faculty.

"But I just hope it doesn’t go on for too long, because I’m trying to graduate in June," she said.

While classes have been temporarily cancelled, York's libraries, labs, cafeterias and athletic centres remain open.

Classes remain on at U of T, despite approximately 6,000 TAs, markers and instructors walking off the job Monday.

The union says the majority of undergraduate courses at the school are taught by non-tenured staff who are paid approximately $15,000 a year.

They say the striking workers want their annual contracts replaced with three-year agreements that will ensure job security.

Ontario's Minister of Training, Colleges and Universities Reza Moridi says the government's main priority at this point is the students' futures.

"We urge the universities and the unions to come to an agreement as soon as possible, keeping the best interests of their students in mind," he told The Canadian Press.

With files from CTV Toronto's John Musselman and The Canadian Press