If Mayor Michael Bloomberg and the teachers’ union do not agree on a new system for evaluating teachers in the next few months then Governor Andrew Cuomo said on Wednesday that he would seek to implement a plan by June 1.

The governor said he will introduce legislation Thursday, in the form of a budget amendment, that would grant the state education commissioner the power to impose a plan on New York City. He announced his intention to propose such a law last month with the support of legislative leaders.

The governor said the law not only would grant the state the authority to impose a plan this year but at any time in the future as well.

“This is in perpetuity,” Cuomo said. “Any year that New York City — the New York City school district — does not have a plan in place, then S.E.D. would come in and put the plan in place.”

A state plan, should the Bloomberg administration and the United Federation of Teachers fail to reach their own agreement, would prevent the city from losing out on another increase in state education aid since the funds are tied to having an evaluation system in place.

“We’ve seen the kinds of plans the state has approved,” said Michael Mulgrew, the teachers’ union president, in a written statement. “We are comfortable with them because they are about helping teachers help kids, which is something that we don’t often hear from the city. So while I would prefer to get to a negotiated settlement, with this in place I know a deal will get done.”

Schools chancellor Dennis Walcott said Wednesday that the city was in continued talks with the unions representing teachers and principals, and that he would work with the governor and unions to ensure that the city had a rigorous evaluation system.

“Hopefully, Governor Cuomo’s leadership will push New York City and its bargaining units to reach an agreement,” said Merryl Tisch, chancellor of the New York Board of Regents, and John King, the state education commissioner, in a joint statement. “But if they can’t meet their responsibility, we stand ready to move forward to meet the parameters the Governor has laid out.”