Minuteman High School is asking the state for more time to win local approval for its new high school.

Superintendent-director Edward Bouquillon sent the Massachusetts School Building Authority a letter on Wednesday asking for an additional 180 days after Belmont Town Meeting members shot down a proposal to pay for a new Minuteman High School.

The $144.9 million school needs unanimous support among its 16 Minuteman member towns. Communities voted this spring, and Belmont was the only town that rejected the project. The vote, on May 4, was 141 against to 81 in favor.

Under an agreement with the building authority, which is contributing about $45 million toward the new school, Minuteman had to win local approval by June 16.

Belmont town officials have consistently questioned the size of the building and the need for space to house 628 students. The school had 673 students as of November, but just 396 were from member towns.

Despite the vote, Bouquillon said he is not giving up. He said support for the school in other communities is strong, so he hopes to persuade the state’s school building authority to extend the deadline for local approval. If the state grants an extension, Bouquillon said, he would use that time to work with Belmont officials and residents to gain support.

“We simply can’t let 30 votes stop a project that literally thousands have voted for,’’ he said. “We feel we have a tremendous amount of support so we need to keep trying. We will engage the stakeholders — town officials, Town Meeting members, community groups — in a more substantial way.’’

Bouquillon said the school isn’t likely to get an answer from the state about an extension until after the school building authority board meeting at the end of June. If an extension is granted, Bouquillon said the Minuteman School Committee will take a vote, similar to one it took in March, approving the project. If a town wants to vote it down, it would have to call a special Town Meeting, Bouquillon said.

“If no town disapproves, then the vote of the School Committee is validated and we can go forward with bonding the new school,’’ he said.

And if Belmont calls a Town Meeting and votes it down a second time, Bouquillon said, the Minuteman School Committee could then call for a district-wide election.

But the state could also not grant an extension, and if that’s the case, Bouquillon said, the project would come to a standstill.

“I don’t know if they will give it or not,’’ Bouquillon said. “If they don’t agree, we’re out of the pipeline and to get back in would take two to three years.’’

Jennifer Fenn Lefferts can be reached at flefferts@yahoo. com.