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 1,” 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.