Allina Health presented a new offer Monday to get the union representing its 4,800 Twin Cities hospital nurses back to negotiations after a weeklong nursing strike.

The health system still demands that nurses at its five Twin Cities hospitals switch from their costly union-backed health plans, but the proposal gives them until 2020 to do so and offers concessions in other areas — such as allowing the union to appoint nurses to workplace safety committees.

"The proposal we are making today shows Allina Health is prepared to have an open, constructive dialogue on the issues that both have identified as important to an agreement," said Dr. Penny Wheeler, Allina's chief executive.

The Minnesota Nurses Association expressed displeasure with the public nature of the offer, but indicated in a written statement that it would review the proposal on behalf of its nurses from United Hospital in St. Paul, Mercy Hospital in Coon Rapids, Unity Hospital in Fridley and Abbott Northwestern Hospital and the Phillips Eye Institute in Minneapolis.

"Our position has been clear from the beginning," the union said in its statement. "Nurses will not take a step backward economically in the next contract."

Allina's proposal to restart contract talks comes as some nurses still await calls to return to work after the seven-day strike that ended at 7 a.m. Sunday. Approximately 200 nurses at United and Unity haven't returned to work, the union said, due to the low number of patients at the two hospitals.

The nurses' union-backed health plans feature higher premiums but low or no deductibles for care — plan designs that are rare nowadays but are popular among nurses who are at greater risk than most workers for on-the-job illnesses and injuries.

Allina wants to move the nurses to the plans it offers other employees, two of which are the exact opposite in their designs: lower premiums but higher deductibles.

Allina noted that 3,800 of the nurses receive coverage through their Allina employment, and that 15 percent of them already elected to enroll in one of the Allina company plans.

Some nurses picketing last week said they were set on defending the union health plans, while others wanted Allina to first come back with concessions in other areas.

In addition to more prevention training and involvement in workplace safety, the nurses want changes in staffing that ensure a minimum ratio of nurses to patients so they have time to provide safe and adequate care.

Allina's offer included 2 percent raises for each of the next three years. The Fairview, HealthEast and Children's health systems provided the same raises in three-year deals they reached with their nurses earlier this year, pacts that left benefits unchanged.

Allina broke from those health systems and took on the union health plans in part due to concerns about a federal "Cadillac" tax on high-cost employer-sponsored plans that will take effect in 2020 to pay for the expansion of health insurance provided by the Affordable Care Act.

Allina leaders believe the taxes will be far more likely and higher for nurses on the union plans. They also estimate $10 million in savings by switching the nurses to the Allina plans, in part by giving nurses financial incentives to use lower-cost forms of care — such as generic drugs instead of brand names — when medically appropriate.

Allina's offer didn't include a specific date to resume negotiations.