JUNEAU, Alaska — Alaska Gov. Mike Dunleavy said he is approving the roughly $1,600 oil-wealth fund check for residents passed by lawmakers this year but views it as a partial payment and plans to press for additional funding.

House and Senate leaders tempered any expectations of a fatter payout and insisted any such discussions need to include consideration of changing the dividend calculation.

Dunleavy, in a video released Monday, said majorities in the House and Senate do not share his position on the Permanent Fund Dividend and paying out checks of about $3,000 this year. Still, the Republican governor said he would fight for more money for the dividend and expected a fall special session focused on the issue.

He said he will not let up for Alaskans “until they receive what they are due.”

Dunleavy spokesman Matt Shuckerow said details of any special session would come later.

Dunleavy, a former state senator, campaigned on a dividend for residents paid in line with a longstanding calculation that has not been followed since 2016 as the state has grappled with a budget deficit.

Lawmakers instead asked him to consider dividends of about $1,600 this year. Last year’s capped payout amounted to $1,600 checks.

Many lawmakers see the calculation as unsustainable and at odds with a law passed last year seeking to limit withdrawals from permanent fund earnings for dividends and government expenses. Senate Finance Committee Co-chair Bert Stedman, a Sitka Republican, said there had been discussions this year about a formula rewrite and possible appropriation of additional funds for checks but an agreement on such a package was never reached.

House Speaker Bryce Edgmon, an independent, said he did not see the House, controlled by a bipartisan majority, approving more money for a dividend without a change in the formula going forward.

Dunleavy has maintained the calculation should be followed until it’s changed and said Alaskans, via a public vote, should get a say on any proposed changes. He did not address the formula change issue in his video.

Traditionally, dividends have been paid using fund earnings according to a formula based on an average of fund income over five years. In 2016, then-Gov. Bill Walker reduced the amount available for checks, an action ultimately upheld by the Alaska Supreme Court, which ruled that, absent a constitutional amendment, the dividend program must compete for annual funding like other programs.

Last year, lawmakers began using earnings to help pay for government costs, causing tension with the dividend program that overshadowed lawmakers’ work this year and contributed to drawn-out regular and special sessions.

The dividend was included in a budget bill passed last month that sought to restore much of the money vetoed by Dunleavy in June. Lawmakers were unsuccessful in securing the necessary votes to override the vetoes but the legislation they passed last month required a lower threshold of support.

In his initial veto announcement, Dunleavy defended his actions as difficult but necessary to respond to a deficit that has persisted amid low-to-middling oil prices.

Ahead of Monday’s announcement, Dunleavy said he would accept restored funding in a number of areas, including certain early childhood learning, legal service and senior citizen programs. He also moderated his position on University of Alaska system budget cuts, saying he would accept a $25 million cut this year — and $70 million in operating cuts over three years — rather than a one year, $135-million cut he had endorsed earlier.

At a news conference announcing the university decision last week, Dunleavy said that action was not related to an effort to recall him from office.

He credited his vetoes with getting residents to talk about what they valued.

Vetoes announced Monday included money for Medicaid, state ferries and public broadcasting. Dunleavy said the state’s fiscal outlook requires rethinking how the state provides services and the way it spends money.

Senate Minority Leader Tom Begich, an Anchorage Democrat, in a statement said Dunleavy’s vetoes “continue to display a lack of vision for this state.”

Dunleavy told reporters last week his intention was not to cause angst or turmoil. He said people saw with his initial budget proposal and his first round of vetoes that he was serious about tackling Alaska’s fiscal problems.