HARTFORD, Conn. — Gov. Dannel P. Malloy on Thursday released a new budget plan that would restore some state aid to cities and towns that he slashed in a previous proposal, in a bid to end the budget impasse at the Capitol.

The Democratic governor said the new plan is a compromise that would increase municipal aid by nearly $900 million compared with the proposal he issued last month. The plan would go into effect only if he and lawmakers can’t agree on a new budget by the end of the month.

State lawmakers have been unable to agree on a budget for the fiscal year that began July 1 and the following year, compelling Malloy to run state government with his limited spending authority. The state, with an annual budget of around $20 billion, faces an estimated $3.5 billion deficit over two years.

Malloy called last month for eliminating state education aid entirely to 85 school districts and reducing school aid to another 54 districts, while 30 of the state’s neediest districts would see no cuts to their aid. Local officials said that plan would have cost many wealthy and middle-income towns millions of dollars in aid and forced them to increase property taxes.

The governor’s new plan would phase in a progressive education funding formula, giving towns facing a loss of school aid more time to prepare.

Before the school year began, many local education officials took severe steps to curb costs including laying off teachers and delaying the opening of school, because of the uncertainty of the state budget and education aid levels.

Hartford Mayor Luke Bronin warned Malloy and lawmakers on Thursday that the city will run out of money in about 60 days and may be forced to file for bankruptcy if the state fails to approve a new budget and continues operating under Malloy’s limited authority.

Malloy said he will release the full details of his new plan on Friday. Legislative leaders said they were waiting to see all the details before debating them.

“There are no easy answers left or rabbits that we can pull out of a magical hat,” the governor said in a statement. “We have to meet one another in the middle and make difficult compromises, and we do it in a way that stabilizes the state’s finances over the long-term. That’s what my budget proposal seeks to achieve.”

Malloy also has scaled back his plan to make cities and towns contribute toward teachers’ pensions. The budget he proposed in February called for cities and towns to pay $400 million of the $1.2 billion annual cost of teacher pensions that is now completely shouldered by the state.

The governor’s new proposal would reduce those new teacher pension costs for municipalities by about $316 million in the current fiscal year and $231 million the following year.