ALBANY — County Executive Dan McCoy said Thursday that city school officials should put Tuesday’s hotly contested Albany High School referendum up for a new vote after widespread voting problems have prompted questions about its legitimacy.

McCoy, who did not take a public position on the high school proposal before Tuesday’s referendum, said a new vote may be the only way to avoid and lengthy and costly legal battle that is the last thing the sharply divided district needs right now.

“This is going to be an ongoing saga if they don’t straighten it out,” said McCoy, who lives in the city’s 8th Ward, one of the hotbeds of opposition to the $180 million new high school. “We need leadership. That’s what we need.”

Pointing to the upcoming presidential primary on April 19 and the annual school budget vote in May, McCoy said the district has two chances to restore public confidence and more time to listen to voters.

Tuesday’s referendum passed by an unofficial margin of 189 votes, or about 51 percent of the total.

“They have two opportunities in front of them — April or May — to redo the vote,” McCoy said, noting that fighting the federal lawsuit being considered by county Comptroller Michael Conners and aggrieved voters will only end up costing the district money, too.

Mayor Kathy Sheehan, a supporter of the project, has said the district needs be held accountable for the voting problems but declined to say whether the referendum should be put up for a new vote. School board President Kenny Bruce said Wednesday there are no plans to do that.

McCoy said his own family members were among those who went to the polls at Mater Christi School only to find the site had run out of ballots, as they did a six other polling places around the city.

“My wife and daughter couldn’t vote. Twice they went there and there were no ballots,” McCoy said. “It’s an embarrassment for everybody.”

McCoy, a Democrat in his second term and an Albany High graduate, said he has never seen the city so divided and that the district should take the time between now and April to try to build consensus on the project.

“We need to heal as a community and come up with a plan that works,” he said. “A lawsuit is just going to muck up the waters. … This is where people need leadership. They don’t need people in there mixing it up.”