MINNEAPOLIS — Union leaders representing about 5,000 nurses in the Twin Cities say members have rejected the latest contract offer from Allina Health, setting the stage for a strike at four hospitals.

The nurses work at Abbott Northwestern, Mercy, Unity and United hospitals. The Minnesota Nurses Association said in a statement late Monday that a majority at all four hospitals voted to reject the contract that many say shifts too much of the company’s health care costs to the nurses.

The statement says members also voted to authorize the negotiating committee to call a strike. The statement says MNA must give the employer a 10-day notice for a strike.

Allina says it wants nurses in a health plan similar to its other employees. A spokesman said Allina was disappointed in the vote and believes continued good-faith negotiations can avoid a strike.