More than 4,000 striking Allina Health hospital nurses will vote Monday on a contract offer that addresses some of their concerns over a shift in health insurance, but does not grant the control their union had sought.

After three daylong negotiating sessions, the Minnesota Nurses Association released a statement shortly before 1 a.m. Friday saying it would put the contract to a vote, but that its negotiating team “is not making a recommendation” whether nurses should accept or reject it.

Allina nurses have voted twice this year on previous contract offers, but in both cases the union recommended rejection; the results led to a one-week strike in June and the current open-ended strike that has now lasted 26 days.

“This decision is now in the hands of our nurses,” Allina said in a statement. “The offer they will vote on represents a true compromise that addresses all the issues raised by the union while offering a fair, respectful transition plan for nurses to the Allina Health core insurance plans.”

The proposed three-year contract gives Allina executives their ultimate prize, a phaseout of four union-backed health insurance plans that they viewed as too costly to maintain. But it offers the nurses some assurances about cost and quality of the alternative plans.

Under the latest offer, the two most popular union health plans would be retained until 2020 and remain unchanged, though Allina would provide bonuses to nurses who switched to one of the company’s health plans in the next two years. Allina also committed to keeping its Allina First plan — so named because it gives incentives to use its own doctors and hospitals — unchanged throughout the three-year contract, and to never change its actuarial value by more than 7 percent in any three-year period.

The proposal also gives nurses 2 percent raises in each of the next three years and a $500 bonus next June.

The vote comes at a pivotal juncture, because striking nurses will temporarily lose their health benefits on Saturday until they return to work.

Nurses picketing outside Abbott Northwestern Hospital in Minneapolis Friday morning expressed disappointment at the proposal and wondered if Allina wanted to test the resolve of striking nurses who are about to lose their health coverage.

“After three days of negotiations, I really thought they would have come out with a contract that we could support,” said Shannon Stenson, an Abbott critical care nurse.

One of the union negotiators, Abbott nurse Angela Becchetti, said the team’s decision not to make a recommendation is an acknowledgment of gains in some areas, but of Allina’s resistance to the union’s health care demands.

“We would offer one solution and they would present five more problems,” said Becchetti, adding that it felt like “we were almost bargaining against ourselves at the end.”

Among the compromises was a provision to address nurses’ concerns about workplace safety; Allina agreed to provide 24-hour security staffing in its emergency rooms.

The union also wanted Allina to free supervisory charge nurses of their direct patient assignments, so they could support front-line nurses in caring for their patients, but the contract proposal only calls for a joint nurse-company committee to address the problem.

Becchetti said one important concession reached during negotiations this week was that a mediator would resolve any disputes that this staffing committee couldn’t work out.

Nurses for months insisted on keeping their union-backed health plans, which feature low or no deductibles, arguing that they are at elevated risk of illness and injury due to the hazards of their jobs.

Nurse negotiators eventually agreed to a phaseout of those plans, but in exchange sought some control over the company insurance plans to assure that their costs and benefit levels didn’t change. Allina rejected the request, though, prompting the nurses to go on strike as of Labor Day.

The prolonged negotiations have taken a toll. Allina’s cost to bring in replacement nurses during the two strikes easily surpassed $40 million. Striking nurses meanwhile were scrambling to find replacement income — hundreds are working at the Ryder Cup this week — and appealing to a union hardship fund.

The absence of guidance from the union bargaining committee on the contract proposal is unusual. In 2010, more than 12,000 Twin Cities nurses were prepared to strike for a second time until their hospitals made last-minute concessions that preserved their pensions and produced a contract that the union recommended.

Becchetti said nurses voting on Monday should decide “what’s best for their families and their practice.”

Votes will be tallied separately for each of the Allina hospitals under strike: United in St. Paul, Mercy in Coon Rapids, Unity in Fridley, and Abbott Northwestern and the Phillips Eye Institute in Minneapolis. That raises the possibility that the strike could end at one hospital and continue at others.

Cardiac nurse Eyobe Woldemariam has been providing paid rides via Uber to earn income during the strike, noting that he has a wife and three small children and also supports his extended family in Ethiopia. But he didn’t see enough compromise in the newest contract offer to support it, even though he already uses an Allina corporate health plan for his family.

“We voted no already,” he said, “and this is the same thing.”