MINNEAPOLIS -- The union that represents thousands of nurses in the Twin Cities metro who are on strike is ready to go back to the bargaining table after rejecting Allina Health's latest contract offer.

The results were announced Monday night following an all-day voting session.

Minnesota Nurses Association spokesman Rick Fuentes says no date has been set to resume negotiations. Fuentes also says it's the union's turn to present an offer to the company, which has also expressed a willingness to return to bargaining.

Union officials didn't direct its 4,800 members on how to vote Monday, as it had in two previous votes. The strike began on Labor Day over health benefits and safety concerns.

In a statement, Allina Health says it's disappointed in the outcome. The company says the proposal was "eminently fair" and addressed many of the issues the union raised during negotiations.

The hospitals affected by the strike are Abbott Northwestern and Phillips Eye Institute in Minneapolis, United in St. Paul, Mercy in Coon Rapids and Unity in Fridley.

Allina released a statement, which reads in part:

The Minnesota Nurses Association announced this evening that nurses at the five striking Allina Health hospitals have voted to reject our latest contract proposal. We offered a wage increase, bonuses, a smooth transition to a sustainable insurance plan and workplace safety provisions the union proposed. This proposal was eminently fair and went very far in addressing the issues the union raised during negotiations. We are disappointed that our nurses will remain on strike instead of returning to the bedside to care for patients.Our top priority is continuing to provide the level of high-quality care that our staff and replacement nurses have been providing since September 5th.

The Minesota Nurses Association also released a statement. Here it is in part:

“In order to get some sort of monetary safety net to protect nurses moving to Allina’s high-deductible health plans, they were asking us to give more away,” said Abbott Northwestern Hospital Registered Nurse and Negotiating Team Member Angela Becchetti. “The nurses saw through that.”

Nurses told Allina negotiators about the continued problems with staffing and proposed to free the charge nurse from a dedicated patient assignment. Allina responded with a staffing committee to look at the issue.

“The nurses felt that although some progress was made in negotiations with Allina it wasn’t enough progress,” Becchetti said. “Nurses felt that the proposal took more away from nurses than it offered. Nurses said they would end their affordable healthcare plans in the year 2020, but they haven’t been adequately compensated for it.”

The latest contract standstill has labor experts wondering how much longer this could go on.

"It’s the classic game of chicken, who’s going to fold first,” said David Larson, labor expert and professor at Mitchell Hamline School of Law.

He says if an agreement isn't reached there is a potential next step.

"The employer can unilaterally implement the contract changes so long as they're consistent with what's been offered in negotiations,” he said.

But because the nurses allege this is an unfair labor practice, he believes that is tricky to do because union members have protections by law in that situation.

Both sides to hold the line but say they are willing to negotiate.

"It’s very expensive for Allina to hire these temporary nurses,” said Larson.

He added it also is very difficult financially on nurses. Allina Health says more than 600 nurses have crossed the picket line so far. The union counters that almost as many have left permanently because of the contract dispute.