The two sides in the ongoing York University labour strife appear to be at a deadlock over how to resolve a dispute that's into its sixth week, with the union asking the province to force the school back to the bargaining table.

There's been little movement between York and CUPE 3903, the union representing more than 3,700 striking members, including teaching assistants, contract faculty and graduate students. They walked off the job at the beginning of March over issues such as predictable employment, workplace equity and access to education.

On Thursday, the union held a press conference to urge the university to return to the negotiating table and call on the provincial government to compel its bargaining unit to do so.

"What we need is for them to come back to bargaining," CUPE Ontario president Fred Hahn told reporters at Queen's Park.

"What we need is for the government to actually publicly say it is time for York to return to a bargaining table. That is the way this will be resolved."

But in a letter dated Wednesday, York president and vice-chancellor Rhonda Lenton appealed to CUPE 3903 chair Devin Lefebvre to agree to arbitration, saying the two sides are at a "point of last resort."

"It appears that we agree that there are significant differences between us in reaching collective agreement renewals," Lenton said in the letter.

"It has become particularly clear to us that we are far apart on the fundamental principles underlying our respective positions."

Lenton went on to say the university has "made all possible good faith efforts" over the last six months of negotiations to achieve a settlement.

CUPE 3903 bargaining team member Lina Nasr countered Thursday that arbitration is indeed a last-resort option, but said that point has not been reached given that the two sides have met only once since the strike began.

"That's not acceptable to say that they have tried and exhausted all their options," Nasr said Thursday during the Queen's Park press conference.