Education Minister Peter Fassbender said government negotiator Peter Cameron advised against such a move.
Fassbender issued a statement on Saturday saying he agreed, calling the teachers' union proposal a "another empty effort" to give parents and teachers "false hope."
Cameron said teachers' conditions regarding class size and support staff levels remain a major stumbling block.
He said he believed the offer was not serious because it did not guarantee the end of the strike.
"They would vote on taking down the strike," said Cameron. "That's not a real proposal."
But the union fired back.
Jim Iker, head of the B.C. Teachers' Federation said arbitration would be a fair way to end the strike and get children back in class.
"Unfortunately, the government continues to put its own interests ahead of all others," said Iker in a written statement. "B.C. teachers are willing to put our proposals to an independent third party for evaluation, but the government remains too entrenched to even consider this fair process."
Iker said the only precondition to bargaining was that government remove a proposal the union says would undo their court losses.
This year the B.C. Supreme Court ruled government breached teachers' rights by stripping them of the ability to bargain for class size and the amount of support staff in classrooms in 2002.
The union accused government of trying to undo that ruling during the bargaining process.
On Friday, teachers said if the province agreed to binding arbitration, they would vote on ending the strike that has delayed the start of school.
Fassbender was cool to the idea, expressing reluctance but stopping short of "categorically" rejecting arbitration.
Cameron's suggestion has cemented the fact the province will not take up the offer.
He said a veteran mediator will be monitoring the situation to see if and when more bargaining can take place.
"I think that's our best line of hope," he said.
"Vince Ready continues to monitor the situation," said Cameron. "At this point Vince does not see any purpose in full-scale mediation happening."
Ready has a reputation for solving even the toughest disputes, but had previously walked out of bargaining sessions between government negotiators and teachers, saying both sides were too far apart.
British Columbia's 40,000 teachers went on strike two weeks before the start of summer vacation, putting half a million students out of class and delaying the start of class indefinitely.