HARTFORD — Connecticut Democratic lawmakers on Wednesday proposed increasing the state sales tax to raise more than $660 million over two years to help curb potential cuts to education aid to cities and towns.

Democratic House members released a two-year, nearly $39.9 billion budget plan that calls for raising the sales tax to 6.85 percent from 6.35 percent. The budget also includes a cigarette tax increase that would raise nearly $80 million over two years.

A House vote on the budget is expected the week of Sept. 11.

Democratic leaders said their plan would ease some of the cuts to local education aid proposed by Democratic Gov. Dannel P. Malloy last week. The governor said he doesn't support the proposed tax increase.

"This is an honest, balanced proposal that reflects the many and diverse priorities of the families and businesses of our state," Democratic House Speaker Joe Aresimowicz, of Berlin, said in a statement.

"No one thinks the governor's executive order is an acceptable option," he said. "So everyone bears the responsibility to get a sustainable budget in place, and this proposal provides a solid basis to move us forward."

The Democratic plan also would allow towns to increase revenue through a new 1 percent local restaurant sales tax, certain local fee increases and other measures.

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.

If a budget isn't approved by next month, Malloy's plan would eliminate state education aid to 85 school districts all together and reduce school aid to another 54 districts, costing many wealthy and middle-income communities millions of dollars each.

Town officials have said the education aid cuts would be devastating and may force them to increase property taxes. Local education officials already have taken severe steps to cut costs, including delaying the opening of school and laying off teachers, with the uncertainty of state aid and the new school year approaching.

The Connecticut Conference of Municipalities, the state's largest organization of city and town leaders, said the House Democrats' plan would cut state aid to cities in towns by more than $120 million statewide, but those cuts would be much less than the "draconian" cuts proposed by Malloy.

Malloy said Wednesday he does not support the proposed sales tax increase. His spokeswoman, Kelly Donnelly, added that the governor also opposes a variety of other revenue increases in the House Democrats' budget and that negotiations on the plan are expected.

Connecticut Republican Party Chairman J.R. Romano criticized the Democratic budget plan on Wednesday.

"They have tripled down on failure, after passing the two largest tax hikes in state history along strict party lines," he said. "With taxes and fees already at historic levels, today's announcement by the Democrats shows their outrageous lack of leadership in serious times for our state."

Democrats hold a slim majority in the House but are evenly split with Republicans 18-18 in the Senate, where Democratic Lt. Gov. Nancy Wyman can break tie votes.