Representatives from the Massachusetts Nurses Association and Brigham and Women’s Hospital are planning to meet Friday to try to hash out a contract deal that could avoid a planned strike on June 27.

Both sides have agreed to meet again with a federal mediator, and Boston Mayor Martin J. Walsh has offered to host the meeting at City Hall. It will be the 20th negotiating session between the hospital and the union and is expected to last all day.

The union represents 3,300 nurses at the Brigham, a large teaching hospital owned by Partners HealthCare. Nurses voted to authorize a strike this week to protest what they call hospital leaders’ disrespect for nurses. After nine months of contract agreements, the hospital and its nurses have been unable to reach agreement on wages, time off, benefits, and other issues.

“Under corporate owner Partners HealthCare, the Brigham cares more about profits and executive pay than providing safe patient care and treating its nurses fairly,’’ Trish Powers, a Brigham nurse who chairs the union’s local bargaining unit, said in a statement. “We are prepared to strike, unless the hospital returns to the bargaining table and offers a fair settlement.’’

Brigham leaders said they stand ready to negotiate. “We’re working very hard to avoid a strike,’’ said Dr. Ron M. Walls, chief operating officer of the Brigham. “We’re hopeful we can get to common ground.’’

Bonnie McGilpin, a spokeswoman for Walsh, a former labor union leader, said in an e-mail that the mayor is eager for both sides to come to a resolution. “He has offered space at City Hall as a venue for ongoing negotiations. The Mayor will not be moderating the discussions,’’ she said.

Asked about the mayor’s offer to facilitate negotiations, Walls said, “We would be open to anything that moves us forward to resolution.’’

Meanwhile, Brigham officials continue to plan for how one of the city’s major teaching hospitals will deal with a walkout by a huge portion of its workforce. Walls said the hospital would scale down operations so it runs at 60 percent of normal capacity. All parts of the hospital would remain open, but elective surgeries and procedures would be rescheduled, he said.

The Brigham is also likely to transfer some patients to other hospitals in case of a strike. It’s unclear exactly how many patients would be affected. Walls said patients will be notified in the coming days.

Since negotiations with the nurses union began last fall, the Brigham has been paying a retainer to a staffing company, U.S. Nursing, to prepare for a possible strike. The hospital plans to hire 700 temporary nurses through the agency in case of a work stoppage and has until Friday to “activate’’ them. At that point, the Brigham will have to pay the temp workers’ wages as well as travel costs.

Brigham nurses are planning a one-day walkout, but the hospital plans to keep them out for five days while using temporary nurses to ensure continuity of patient care.

Walls declined to say how much a strike would cost the hospital, except that it was many millions.

“We’ve already spent millions of dollars through these negotiations,’’ he said.

Meanwhile, six city councilors are urging both sides to settle on a “fair’’ contract. “As a nonprofit health care organization, BWH/Partners should invest its enormous wealth back into the community it serves and the nurses who provide the majority of the care at the hospital,’’ the councilors said in a letter to Brigham chief executive Dr. Elizabeth G. Nabel.

The letter was signed by District 8 Councilor Josh Zakim, District 6 Councilor Matt O’Malley, and at-large councilors Annissa Essaibi-George, Michael Flaherty, Ayanna Pressley, and Michelle Wu.

Nabel responded that the hospital has already offered generous wage increases and benefits. “Our proposed increases would ensure that BWH nurses continue to enjoy a wage scale that is among the most favorable in the city, region, and country,’’ she said.

Brigham nurses receive 5 percent annual raises for their first 18 years on the job. The hospital has proposed giving most nurses an additional 1 percent increase over three years. Nurses already at the top of the pay scale would receive a 1.5 percent increase, plus a $500 bonus.

The union is seeking a 4 percent raise over 18 months, on top of the existing step raises. The average Brigham nurse makes $106,000 a year, plus benefits.

Unless the hospital and the union reach a deal, nurses have promised to go on strike, starting at 7 a.m. on June 27.It would be the first nurses strike at a Boston hospital in 30 years.

Priyanka Dayal McCluskey can be reached at priyanka.mccluskey@globe.com. Follow her on Twitter @priyanka_dayal.