ANCHORAGE — Facing a multibillion-dollar deficit, the Alaska governor on Wednesday cut in half the annual checks that give all residents a share of the state’s oil wealth, but he kept enough money in place to award everyone a $1,000 payout.

Gov. Bill Walker had said recently that all budget-cutting options were on the table, raising the prospect that he might do away with the checks entirely. They have been distributed for more than three decades and last year climbed to a record $2,072.

Alaska’s government relies mostly on revenue from oil production to stay solvent. But declining production and a precipitous drop in oil prices have left the state with a deficit of more than $3 billion for the next budget year.

If changes are not made, Walker said, the oil-wealth program could disappear. He urged lawmakers to find a solution during a special session that starts July 11.

Walker’s reduction of the oil-check purse was among $1.3 billion in budget vetoes that he said would result in savings across much of state government. He compared the cuts to running through fire.

“The fire is the future of Alaska,” the governor said.

After a news conference, Walker told The Associated Press that he runs the risk of having lawmakers override his budget vetoes, but that’s not his intent.

“You know, I’ve pulled them back in special session so we can finish the job. If they take that time to override my vetoes, there’s nothing I can do about that,” he said. “I’ve done everything I can do.”

Walker has proposed several measures to help bridge the gap, including tapping into the oil-wealth fund, which has paid a dividend yearly since 1982.

Walker’s decision leaves lawmakers in an awkward position. They must either approve his proposal to cap the checks at $1,000 or risk issuing no checks at all just months before the fall election.

Associated Press Writer Rachel D’Oro contributed to this report.