ST. PAUL — Minnesota lawmakers on Thursday found a way out of a state agency salary fight that had them tied in knots, reaching a deal that suspends commissioner raises but still gives Gov. Mark Dayton a one-day window to hike pay this summer.

The agreement approved 106-21 in the House heads next to the Senate, which won’t act until next week. The bill returns pay for state agency heads to last year’s levels and keeps it there until June 30, temporarily wiping out big increases Dayton granted last month.

Dayton could enact new raises on July 1. If he waits until July 2, those raises would be subject to legislative signoff.

“All eyes will be on the governor on July 1st,” said Republican Rep. Steve Drazkowski of Mazeppa. “Is he going to be with us or is he going to be exercising the same type of crony behavior he did last time?”

Democrats said Republicans were talking tough about cutting pay while still giving Dayton room to pay his commissioners more. But they also were glad to dispense with an issue that had consumed the Capitol and caused friction within the upper ranks of their party.

“I’m hopeful that this puts the issue to rest for the rest of session,” said House Minority Leader Paul Thissen, a Minneapolis Democrat.

In reaching the pact, the Legislature is also removing an obstacle to a $15 million stopgap spending bill to which the pay issue became entwined. There is urgency because the bill includes time-sensitive funding for Minnesota’s Ebola response, the St. Peter security hospital for sex offenders and other mentally ill patients, the Minnesota Zoo and the Department of Natural Resources.

All of that got overshadowed by the moves to temporarily block the Dayton Cabinet raises. In January, Dayton exercised authority given to him in 2013 to push up pay for commissioners already earning six-figure salaries, up to $30,000 more per year in some instances. The raises totaled $900,000 per year.

The governor has defended the move as making the positions competitive with those in local government and private-sector posts with comparable responsibility. With some exceptions, pay for the jobs had been stagnant until lawmakers modified a hard salary cap for the jobs two years ago.

The new bill would freeze pay and would modestly reduce a few agency budgets to account for salary already paid out. But it wouldn’t require the commissioners themselves to give back higher pay they’ve received since the start of the year.

Dayton had been threatening to veto the spending bill if lawmakers meddled too much on executive compensation. But Senate Majority Leader Tom Bakk and House Speaker Kurt Daudt said Dayton backed down. Dayton’s office wouldn’t comment beyond a statement issued Wednesday that said he was anxious to move beyond the pay flap

“Obviously I got the better end of the negotiations,” Daudt said. “But at the end of the day if the governor continues down the path of raising these salaries, Minnesota suffers.”

Daudt said he hopes Dayton uses “some discretion and not spring them back to what they were.”

Relations between Bakk and Dayton — the Capitol’s two most-powerful Democrats — particularly soured after the Senate leader led a charge to suspend the raises, a move the governor said he didn’t expect. Dayton labeled Bakk untrustworthy; Bakk said the two had a mere miscommunication.

“We’ll probably be a little more careful communicating with each other going forward and I think that’s probably a good thing,” Bakk said Thursday, adding, “You cannot let things get personal because there’s always another issue to work through.”