Labor unions representing thousands of city workers in Oakland said they will go on strike starting Tuesday, interrupting nearly all non-emergency services with the first major walkout in the city in four years, after negotiations came to a halt Monday.

Mayor Libby Schaaf said the strike would be unlawful because the two parties have not mutually declared an impasse. She said the city would file a labor complaint if workers walk off the job. But leaders for Service Employees International Union Local 1021 dismissed Schaaf’s concerns.

“The mayor is incorrect,” said Rob Szykowny, Local 1021’s chief negotiator. “It’s an unfair labor practices strike, which is lawful, protected activity.”

A UC Berkeley lecturer in labor law whose Alameda practice represents Local 1021 agreed with the union.

Photo: Mike Kepka, The Chronicle

“A public-sector union has a right to strike in this context because I assume there’s no contract in effect and they haven’t reached one. That’s basic public-sector law,” David Rosenfeld, the lecturer, said. “I don’t know what the city’s problem is.”

Local 1021 represents Oakland librarians, street cleaners, sewer workers, parking enforcement officers and others. The union proposed Monday to bring in as an informal mediator former San Francisco Mayor Willie Brown — a Chronicle columnist who’s previously refereed BART labor disputes. But the city rejected that offer.

“Willie Brown convened politicians on behalf of the union several months ago,” Schaaf said, adding that she was “disappointed” in the union for planning to strike. “I love Willie Brown. I have tremendous respect for him. But he does not appear to be neutral in this matter.”

The union, which has been without a contract since June, agreed with the city’s first-year contract proposal, which would increase wages by 4 percent, retroactive to July 1. The parties dispute what should happen next: The city has offered future salary increases tied to its revenue growth, but the union wants the city to commit to another 4 percent increase the following fiscal year.

Photo: Justin Sullivan / Getty Images

Had the city agreed on a one-year deal or to Brown as mediator, Szykowny said, the strike would have been canceled.

Karen Boyd, a city spokeswoman, said the city hadn’t gotten the opportunity to present the latest proposal to the City Council for consideration. The council is scheduled to meet Wednesday, which city officials said was the soonest legally possible time.

“It baffles me,” Szykowny said. “All they have to do is sit in the room in good faith, and it’s shocking they wouldn’t want to do that.”

Other labor conditions — overtime, use of part-time workers, retention problems, vacancies, and health and safety concerns — are major issues that need to be addressed, according to union members. They say their peers are fleeing Oakland for better-paying but identical jobs in nearby cities.

“We were able to get some really good noneconomic agreements, but when you get down to money, it really starts to get challenging,” said Lauren Takeshita, an Oakland police administrative analyst and member of a sister union, which will also go on strike. “It’s their role to say no, which they unfortunately are doing very well. It’s our role to say, ‘Why not?’ and ‘How come?’ and ‘Be fair.’ We continue to chip away at it, and we continue to ask them to be reasonable.”

Rising costs of pensions and employee health care are outpacing the city’s revenue growth, Boyd said.

“We cannot spend money we do not have,” Schaaf said. “We have to preserve basic services for Oaklanders — not just today, not just tomorrow — but for the long term.”

The city gave Local 1021 its “best and final” offer Friday and said if any portion were rejected, the entire proposal would be considered null. Schaaf, who has been the target of much of the union’s displeasure and its advertising campaign, said Monday night she was still hoping to avoid a strike.

“This will have an impact on so many Oakland residents, particularly vulnerable residents,” she said. “We are continuing to ask labor to wait until we have an opportunity to present their offer to the City Council.”

Local 1021 members overwhelmingly voted in late October to give its bargaining team the authority to call a strike. Another union, International Federation of Professional and Technical Engineers Local 21, approved a solidarity strike. And a third, the International Brotherhood of Electrical Workers Local 1245, said its members would not cross the picket line.

About 3,000 workers were expected to strike Tuesday starting at 7 a.m.

City Council committee meetings were canceled for the week. Nearly all nonemergency city services — child care programs, libraries, senior centers, parking enforcement, fire and building inspections, street sweeping and more — were suspended for Tuesday.

Police officers and firefighters are barred from participating in the strike, and emergency dispatchers will come to work too. The Oakland Animal Shelter and the city’s website, including its online bill-collection services, will also remain open.

Kimberly Veklerov is a San Francisco Chronicle staff writer. Email: kveklerov@sfchronicle.com Twitter: @kveklerov