Gov. Mark Dayton and Senate Majority Leader Tom Bakk finally cooled their high-profile feud Wednesday. Using their first private conversation since a blowup two weeks ago to mend fences, the two men agreed that they have too many shared priorities as DFLers to let a dispute about commissioner pay raises fester in public.

In clearing the air, Dayton and Bakk also got on the same page with House Republicans in settling on a path out of the political flap over Dayton's recent decision to give his cabinet officers big pay raises. Under that agreement, headed for House and Senate floor votes Thursday, the raises are on hold until July 1, when Dayton could reinstate them.

But that's the last time Dayton could grant such raises unilaterally: To end the dispute, he agreed to surrender the authority lawmakers gave him two years ago to make such decisions himself.

Dayton's aides wouldn't say whether he intends to reinstate the raises, which totaled nearly $900,000 a year for 30 commissioners.

The decision quickly became an albatross for Dayton, earning scorn from GOP lawmakers and even some Democrats. And it drove a wedge into an already-tense relationship between Bakk and Dayton, who called out the majority leader in public as a conniver and backstabber after Bakk led an effort in the Senate to rein in the increases.

Dayton hosted Bakk and other top DFL lawmakers at a private breakfast Wednesday morning at his Summit Avenue residence. It was the first time he and Bakk were in the same room since Dayton's biting comments.

Dayton "actually put his hand on my shoulder and I put mine on his," said Bakk, DFL-Cook.

He went on: "The governor and I just have way too much work to do to be at odds with each other. I think we're fine." Bakk said they agreed to jointly appear at a March 5 news conference to tout a DFL plan to raise gas taxes for transportation.

Dayton spokesman Linden Zakula had less to say about the meeting, calling it "congenial and constructive." Dayton was not available to reporters Wednesday.

Dayton initially defended the raises as necessary to recruit and retain top talent to state agencies that in some cases have thousands of employees and annual budgets of millions or even billions of dollars. But the issue quickly became an unwanted distraction for Dayton, who unsuccessfully tried to turn the focus of the session back to issues he said were of more wide-ranging impact, like transportation and school funding.

After Dayton and Bakk's relationship melted down, Republican House Speaker Kurt Daudt stepped in to help seek a way out. The issue got attached to an unrelated stopgap spending bill that distributes about $16 million to several state agencies that encountered unanticipated costs in recent months.

That includes money for the Department of Health to pay for its Ebola response, to help resolve a staffing crisis at the Minnesota Security Hospital in St. Peter, and to help the Minnesota Zoo with an operating shortfall.

Late Wednesday, a House-Senate conference committee adopted the Daudt-Dayton-Bakk compromise language on pay raises. Daudt and Bakk said they and Dayton agreed on the provisions of the bill.

The pay dispute initiated a wide-ranging debate in the conference committee about pay for public officials. Several Republican lawmakers said lawmakers in 2013 never should have surrendered legislative oversight to the executive branch.

"This is something that should be done at the legislative level," said Rep. Jim Knoblach, R-St. Cloud.

Several Democrats, while cautious about defending the size of the raises — some commissioners saw pay hikes of $35,000 a year — said it's out of whack when an official like the commissioner of human services, who oversees billions of dollars in state and federal spending, makes the same amount as the city manager in Eden Prairie.

"When you do see the pay at local levels of government — cities, counties, school districts — that are lower in responsibility than many agency commissioners, it does strike me that you're putting the state at a significant disadvantage," said Sen. Dick Cohen, DFL-St. Paul.

If the House and Senate vote Thursday, the bill could be on Dayton's desk by Friday.

Bakk, who earned Dayton's ire with his criticism of the size of the raises, now says he thinks that come July 1, Dayton might be wise to restore the raises at their full amount.

"It's the only increase they're going to get in the rest of his tenure," Bakk said. But he left no doubt who he sees bearing any remaining political fallout.

"If this is something the governor decides to do, I think the governor is going to own it on July 1," Bakk said. "We talked about that. He's perfectly fine with that. This is his decision."