Long-simmering tensions over policing in Toronto have come to a boil, with the new mayor, John Tory, accusing the police board chair of inflaming the situation with a controversial Facebook post, and the union calling for the chair to resign over it.

In recent months, the already strained relationships among the police board, the chief and the union in Canada's largest city have descended into full-scale hostility over issues related to policing costs, and ahead of contract negotiations.

After winning the October election on a promise of bringing the city together, Mr. Tory has pledged to repair what he views as the "increasingly polarized" relationship between the police board and the force itself.

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That animosity was in full view Friday, after board chair Alok Mukherjee posted a photo to his Facebook wall comparing the death toll caused by American police officers with those of the terror group Islamic State, also known as ISIS, and Ebola.

"Americans Killed by ISIS: 3, Americans Killed by Ebola: 2, Americans killed by the police: 500+ every year," read the post shared by Mr. Mukherjee. "Just a reminder of who the enemy is in the world" read the caption – written by the post's original author, Occupy Wall St.

The Toronto police union wants the chair of the board to resign for posting this link on his Facebook page. pic.twitter.com/Jwj5650owP — robyndoolittle (@robyndoolittle) December 5, 2014

The reaction was swift, with police union president Mike McCormack slamming the chair as "biased," and Mr. Tory – who last week pledged to personally sit on the police board to help ease tensions – saying he will need to have "further discussion" with the chair, and describing it as "an error in judgment."

"I think it just inflames situations here in Toronto that don't need to be inflamed," Mr. Tory said.

Initially, Mr. Mukherjee told The Globe he was surprised by the reaction, and said his post had nothing to do with policing in Toronto.

"My intent in putting that poster on my Facebook was to trigger conversation and thinking about the differences between what we face here and what's happening in the U.S. In fact, our response has been very, very different," he said.

But after coming under pressure to explain the comment, including a call from the mayor, he issued a statement expressing regret for "the reaction caused by the posting" – although he stopped short of an apology.

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"The share was not meant as an endorsement of any views contained," he wrote. "I have the utmost respect for members of the Toronto Police Service and I strive at all times to serve as chair in a fair and professional manner."

Mr. Tory said he did not think the chair's statement went far enough, and pointed to the exchange as "one more example" of why he wants a fresh start with new members on the board. The board is also searching for a new chief to replace Bill Blair.

Mr. Tory would not say whether he thinks Mr. Mukherjee should remain as chair, but that position is up for grabs next month when the seven-member board, which includes Mr. Tory and two newly appointed councillors, vote on the positions of chair and vice-chair.

Mr. McCormack said the chair should resign. "It clearly demonstrates to me that he has no objectivity, that he's biased against policing, and that he lacks total judgment."

Councillor Michael Thompson, a former member of the police board who was not reappointed by the mayor, characterized the union's calls for the chair's resignation as a negotiating tactic. "Remember, we are in a process with respect to negotiation," he said. "I think that it's like everything else; you use all the ammunition you can actually find, and this is part of that particular process."

Friday's back-and-forth came the same day city councillors raised questions about a dramatic drop in the number of traffic tickets issued by police this year. Traffic ticket revenue is down 35 per cent and expected to leave the city with a $25-million hole it its budget. Mr. Thompson said ticket revenue began to decline in 2013, suggesting police were retaliating for the first year of a budget freeze.

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Chief Blair would not respond to either Mr. Mukherjee's or Mr. Thompson's comments.