The union that represents 3,000 workers at Allina Hospitals is trumpeting a three-year contract that it says for the first time establishes a $15 minimum wage.

Allina, without commenting directly on the assertion by the Service Employees International Union (SEIU), said Friday that it has agreed to a contract that pays 3.5 percent in wage increases over three years and that 97 percent of the affected workers already make at least $15 an hour.

“We are pleased to have reached this agreement with the SEIU,” said David Kanihan, an Allina vice president. “The new contract is a good deal for our employees, for Allina Health and for the communities we serve.”

The SEIU, which represents thousands of lab assistants, nursing assistants, kitchen and other staff at Allina and other Twin Cities hospitals, also is a lead organization in the public campaign for $15 an hour minimum wages in the fast food industry in the Twin Cities and other metropolitan areas.

A spokesman for the union didn’t dispute Allina’s statement that most of the workers already make more than $15 an hour plus benefits. However, David Zaffrann, communications director at SEIU, said the significance of the member-ratified deal with Allina is that it establishes a $15 minimum wage at six Allina Hospitals in the Twin Cities, including Abbott Northwestern, as well as the pay increase.

The union said the contract provides employment security protections as well as additional health and safety protections, an increase in ­Allina’s contribution toward the members’ pension plan, and a 25 percent increase in the amount of tuition reimbursement available to members annually.

Allina, the largest hospital system in Minnesota, said the contract includes annual raises of 2 percent, 1 percent and 0.5 percent over the three-year term.

SEIU-represented employees approved a three-contract for several thousand other workers, which included a 4.5 percent raise over the term, in February, following joint bargaining with Children’s, North Memorial, Fairview and other hospitals owned by HealthPartners.