MILLINOCKET, Maine — Voters rejected the school system’s proposed $6.2 million budget on Tuesday night by 10 votes, officials said.

According to unofficial vote totals released Tuesday night by Town Clerk Roxanne Johnson, 375 people voted in favor of the budget and 385 voted against it during the validation vote. The number of votes cast represents about 22 percent of the 3,320 registered voters in town.

Millinocket School Committee Chairman Kevin Gregory, who urged voters to reject the budget because of Town Council cuts to it, did not return a message left Tuesday night.

Council Chairman John Davis said he got some satisfaction from the 10-vote margin.

“We are getting closer,” Davis said Tuesday. “It was a great turnout and it looks like we are going to be doing it [voting on another budget] again.”

Facing a $3 million to $4.5 million cash shortfall, councilors voted 4-2 last week to pare $322,000 from the school department’s budget from the school department’s $6.6 million proposed budget for the 2013-14 fiscal year, which began July 1. Councilors Michael Madore and Richard Angotti Jr. opposed.

Superintendent Kenneth Smith has said the $6.2 million budget left by the cut would harm education by forcing the elimination of five teacher positions and three programs.

Councilors and school board member Matthew Farrington said they believe the cutting of the $322,000 from $644,000 in medical benefits the school department pays retirees would not harm the education provided students.

School board members said that cut cannot legally be made unilaterally. Gregory said the cut was against everything he stands for. Councilors said they dislike paring retiree benefits but felt the cut was essential because, they felt, it would not impact students’ education.

Davis said he interpreted the narrow margin as supportive of the council’s position. He said he doubted that the council would change its position when the budget process restarts and school officials present councilors with another budget.

“I really don’t know for sure. It is something that we are going to talk about,” Davis said. “We got a serious problem with cash flow.”