ST. PAUL — Minnesota Gov. Mark Dayton and state lawmakers emerged from a private meeting with a federal judge on Monday with little consensus on how and even whether to forge ahead with changes to a state program confining sex offenders that the court has deemed unconstitutional.

Joined by more than a dozen Minnesota lawmakers as well as other state officials to discuss the program’s future, Dayton said no decisions were made during the three-hour conference with Judge Donovan Frank. Frank is prodding the state to take action to rework the program, which indefinitely houses more than 700 offenders considered “sexually dangerous” and a threat to reoffend, before he requires action.

The conference, held in private despite media protests, stems from a class-action lawsuit brought by offenders who have been committed to the program by a court apart from any criminal sanctions.

Dayton said he still believes the program is constitutional and is looking for an avenue to appeal Frank’s June decision after the judge comes out with a directive telling the state what must be done. That order is expected this fall.

“I believe he understands the sensitivity of the matter, the potential for controversy and most importantly the need to protect public safety and security,” Dayton said of the judge, adding that achieving a legislative solution could be difficult given election-year politics that will be in play in 2016.

In the meantime, the governor has some fixes in mind — a new evaluation system to periodically review offenders, combined with building less-restrictive facilities for lower-risk inmates with medical needs — that together could cost $20 million or more a year in addition to what the state spends now. The 2016 fiscal year budget for the program is about $84 million, reflecting the estimated $120,000 per offender, according to the Department of Human Services.

Republican House Speaker Kurt Daudt put the onus on Frank to act first, and said “the Legislature may or may not have to take action after that.”

Some lawmakers at the meeting said the judge seemed most interested in finding alternatives for sex offenders who are juveniles, elderly or cognitively disabled. Among them are patients who have never been convicted of a crime, but civilly committed to the program instead.

Sen. Ron Latz, a Democrat who chairs the Senate Judiciary Committee, said placing offenders into less-restrictive settings would still subject them to intensive supervision to keep track of their whereabouts and habits.

“No one is talking about opening the door and letting people walk out no matter what the judge orders, and he made clear he wasn’t going to order that,” Latz said.

The legal challenge to Minnesota’s program has sparked interest in the 19 other states with similar programs. Cynthia Calkins Mercado, who has studied the issue at the John Jay College of Criminal Justice in New York, said Frank’s earlier ruling is the most sweeping condemnation of a state sex offender system. But she said it could implicate programs, “especially those states that have exceptionally low release rates, unclear release criteria, or those that fail to tie treatment progress to likelihood of release.”

The timing of potential changes in Minnesota is cloudy. While Dayton said any solution may require a special session of the Legislature to create a new evaluation system and fund new buildings, Daudt said it could wait until the Legislature is set to convene in March or even later.

If an appeal goes forward, plaintiff attorney Dan Gustafson said that could push any resolution to the case out up to 18 months.

“It’s very frustrating to my clients because they hear the judge say in June that it’s unconstitutional, and now we’re in August and nothing has changed,” Gustafson said.