MINNEAPOLIS  — Democratic Gov. Mark Dayton pledged Saturday not to take a salary if the state government shuts down next month, and said it would be “terribly wrong” for him or any Republican legislators to collect a paycheck while other state employees were denied their own.

State leaders say they’re trying to avert a government shutdown, but they’re also making plans to ensure they get paid if a deal isn’t struck in time. The GOP-controlled House has assured lawmakers and staffers they’ll still receive paychecks, even as thousands of government workers prepare for a temporary loss of income.

House staffers told members they can refuse their pay. House Majority Leader Matt Dean, R-Dellwood, said he hadn’t yet considered yet whether he would do so.

Dayton released a statement Saturday saying he wouldn’t collect a paycheck.

“In the event of a state government shutdown, which I remain committed to doing everything possible to avoid, I think it would be terribly wrong for those of us responsible for it, the Republican legislators and myself, to receive our salaries while thousands of dedicated state employees have lost theirs,” he said.

Dayton and the GOP-controlled Legislature are at odds over how to set a new two-year-budget. The governor wants to raise income taxes on Minnesota’s highest earners, while the GOP is proposing spending cuts.

If no budget is approved by the end of the month, the state will lay off thousands of workers and cast doubt over billions of dollars in payments, including money for health care, schools and government aid.

But House staffers told members this week that the law requires legislators be paid on the first of the month. In the event of a shutdown the House plans to make those payments from money already in the bank.

The Senate has enough stored cash to pay its members through mid-July, and will resort to furloughing staff after that, said Cullen Sheehan, chief of staff for the Senate Republican majority.

Dayton and other constitutional officers did not get layoff notices, as 36,000 state employees did, said governor spokeswoman Katharine Tinucci. That means he’d keep working even if a shutdown occurred. He asked the courts this week to also let 21 of his staffer keep working — and receiving paychecks — even if much of the government closes.

The court will ultimately decide what money the state could spend in a shutdown.

Jodi Boyne, a spokeswoman for House Republicans, said lawmakers there will seek permission to spend the $4 million in the bank to keep salaries flowing. That amount would keep the House fully funded until the beginning of September.

Other groups are also lining up to ensure certain funds remain in play. The judicial branch and attorney general are asking that courts be kept open during a shutdown. The League of Minnesota Cities plans to ask that payments to cities be continued, and health care providers are expect to ask that their services be declared essential and hence worthy of payment.