The University of Toronto may risk infringing on one of its core values if it seeks to stop psychology professor Jordan Peterson from further declaring that he will not use gender-neutral pronouns, says the national association for university faculty.

Dr. Peterson has been at the centre of a growing debate on campus over whether remarks he has made repeatedly over the past few weeks on YouTube are leading transgender students, faculty and staff to feel unwelcome and unsafe on campus. Last week, the university issued a warning about threats made by trolls on social media against members of the transgender community.

On Tuesday, senior administrators at the U of T renewed their call to Dr. Peterson to stop making statements that could be considered discriminatory under provincial human rights legislation, sending him a letter asking him to cease repeating such remarks. His own department chair made a similar appeal to him earlier.

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But whether what Dr. Peterson has said is the kind of speech that can be limited under Canadian legislation is up for debate, said David Robinson, the executive director of the Canadian Association of University Teachers.

"The onus is on the university to prove that his refusal to use certain pronouns constitutes a violation of law," Dr. Robinson said.

The Supreme Court of Canada has made it clear that some types of speech may be hurtful and an affront to dignity without rising to the level of hate speech, he said. That ruling came in the 2013 case of Bill Whatcott, an anti-gay campaigner in Saskatchewan.

"In the context of a university, we believe that academic freedom and free expression is a core foundational value. There would have to be serious illegal expression that would justify any limitation," Dr. Robinson said.

In the letter to Dr. Peterson, two senior administrators remind the tenured professor that some students have reported they received specific and targeted threats. "We trust that these impacts on students and others were not your intention. However, in view of these impacts, as well as the requirements [of legislation], we urge you to stop repeating these statements," the letter says.

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The university's resolve will likely not be tested until the winter term when Dr. Peterson is teaching several undergraduate courses. If a student made a request to be referred to by a gender-neutral pronoun in the classroom he would likely decline, Dr. Peterson said in an interview. "I guess I would say no, then I am probably prosecuted for a hate crime, that would be my guess."

For the university to suggest that his words could lead to threats is absurd, he said. "How can the fact that I said that we are being a little hasty in making discussion about gender illegal be responsible for unsafe conditions on campus?"

Few transgender students will be talking to him at all, predicted Cassandra Williams, an executive member of the university's undergraduate students' union. "Students don't have thousands of dollars to spend on seeing 'Oh, maybe this professor is going to discriminate against me.'"

She said the university should be stating its next steps and that Dr. Peterson should retract his videos on YouTube and apologize.