The three mayors said Friday they have sent a letter to the prime minister, asking him to call an emergency meeting between the two parties.
"As mayors, on behalf of our citizens, we call upon your leadership to urgently convene a meeting of the parties concerned in order to find solutions that would respect the spirit of the law, thereby protecting the thousands of jobs directly and indirectly affected," said the letter.
"In so doing, we would maintain the Canadian aeronautics industry's rank as one of the best in the world as well as help consolidate the country's economic performance."
The letter was signed mayors Gerald Tremblay, Hazel McCallion and Sam Katz.
"We have spoken to the president of Air Canada and he has expressed a desire to collaborate and to participate in discussions," the letter also said.
The mayors said the closure of Aveos leads to the termination of 3,300 direct and indirect jobs and Air Canada has the obligation to maintain the maintenance and repair centres in Montreal, Winnipeg and Mississauga.
They called the situation unacceptable.
"In the current, fragile economic situation we are experiencing, it is our duty to safeguard the leading edge technology infrastructures and jobs that make Canada one of the worldwide leaders in the field of aeronautics," the mayors said in their letter.
"Even more fundamental is the necessity to respect rule of law as well as the laws upon which this country built both its prosperity and its trust in itself."
The mayors said Air Canada is not a private company like any other, as it is the country's national air carrier.
"Its obligations under law come as a compensation for the protection of its privileges as such. This has also, and very recently, enabled your government to intervene in the carrier's labour relations."
Air Canada was transformed from a Crown corporation into a private company in 1988.
Aveos Fleet Performance recently announced its liquidating its Canadian aircraft maintenance business, putting virtually all of the company's 2,600 employees across the country out of work.