JUNEAU, Alaska — Gov. Bill Walker favors a law to limit how much lawmakers can pull from the earnings of Alaska’s oil-wealth fund to pay for state government and yearly checks to residents.

Walker told reporters Tuesday that a lack of such a structure could be risky for the fund’s sustainability.

He would not say whether he would he would approve a budget that relies on a limited draw from Alaska Permanent Fund earnings if a law making a structured draw permanent isn’t passed.

“We will evaluate that at the end of the process,” he said.

The House, as part of the operating budget it passed for the coming fiscal year, proposed taking $1.7 billion from fund earnings to help cover government costs and another $1 billion for the annual dividend check Alaskans receive from the oil-wealth fund.

The amount was based on a draw equal to 5.25 percent of the fund’s average market value over the prior five years, according to the House majority. House Finance Committee Co-Chair Paul Seaton called that level of draw “sustainable on a short-time basis.”

The House budget also proposed taking about $700 million from a state savings account to help fill the deficit but fell short of the level of support needed to tap that fund.

Traditionally, dividends have been paid with fund earnings, based on a calculation set in law. But that formula has been ignored the last two years, and dividends capped, amid legislative gridlock over how best to fill the deficit.

The House proposal would set the dividend at $1,600 per person, compared to an estimated $2,650 had the formula been followed. The Senate has yet to propose its version.

The two versions of the budget are typically reconciled between House and Senate negotiators.

Walker said he was “not uncomfortable” with the dividend amount proposed by the House.

In a newsletter Monday, Walker said a draw limit “must be binding in law.” He also said need for government services or an aversion to taxes cannot be allowed to eliminate future dividend funding, and called for an “unbreakable floor” for dividend amounts.

Some use of permanent fund earnings is widely seen as necessary to help fill the budget hole. Walker and legislative leaders have envisioned some type of draw based on an average of the fund’s market value, versus just taking cash out without parameters.

But the House majority, composed largely of Democrats, and the GOP-led Senate have disagreed on what additional actions need to be taken.

House leaders believe other measures, such as a broad-based tax and changes to oil taxes, should be part of an overall fiscal plan.

The Senate rejected an income tax last year and has been lukewarm to revisiting oil taxes, maintaining that the deficit can be managed with fiscal discipline.

On Tuesday, House leaders were noncommittal about Walker’s proposal to set a draw limit in law.

Rep. Neal Foster, a Democrat from Nome, said he doesn’t see that as a must-have for ending the session, “under the current circumstances, without a full fiscal plan and so forth.”

House Speaker Bryce Edgmon said there have been preliminary discussions with Walker’s administration on the Legislature’s remaining work. The session is scheduled to end in less than two weeks, but Edgmon said lawmakers probably will need more time.