The strike threat comes one day after teachers in Durham Region hit the picket lines, leaving 24,000 students out of class.
The Ontario Secondary School Teachers' Federation said Tuesday that teachers in Peel, west of Toronto, will go on strike May 4 if a local collective agreement is not reached with the school board by then.
There have been only six bargaining sessions since January, with little progress to report, and patience is wearing thin, the local union president said.
"All we've agreed to up to this point are items that both sides believe are status quo...and a few housekeeping items," Mike Bettiol said.
Education Minister Liz Sandals has said she is "perplexed" by what local issues could have driven teachers in Durham Region to go on strike Monday and for other boards such as Peel to threaten job action.
The head of the Peel District School Board, which has about 42,000 students, went further, suggesting the local strike is really about putting pressure on provincial negotiations, where monetary issues are being discussed.
"Nothing could be further from the truth," said Bettiol, though he would not detail what local issues are prompting the union's strike threat.
"They mostly have to do with the ability of our members to exercise their professional judgment when they teach kids."
The chair of Peel's board said the union is being "deliberately misleading" in making it seem like the strike is about local issues.
"No local action was needed to keep us at the table — we are there and want a settlement," Janet McDougald wrote in a statement. "The reality is that this is a provincial strategy with a harshly negative local impact for our students. Our students are being used by OSSTF provincial as pawns in their strategy."
This is the first round of negotiations since the Liberals — who are trying to eliminate a $10.9-billion deficit — brought in a new bargaining system, with both local and provincial talks.
Sandals said under the new system, local strikes must be over local issues, which she said she has not seen clearly articulated.
"What I have not heard is what's the local issue that this strike is over?" she said Tuesday. "That doesn't mean that there aren't local issues. Obviously there are local issues or presumably they wouldn't be on strike, but (those haven't) been clearly identified."
Centrally, talks resumed Monday between the high school teachers and the province, while the elementary teachers have said their central talks are at an impasse.
The Peel strike date is the third set locally by the OSSTF, with teachers in the Sudbury area — in the Rainbow District School Board — set to walk out April 27.