Lawyers with the Legal Aid Society in New York City, the state’s largest provider of criminal and civil legal services for indigent clients, were locked in a struggle for higher pay Monday after authorizing their union to strike.

If negotiations fail, members could walk off the job for the first time in 30 years, leaving the courts scrambling to cope with the sudden absence of more than 1,000 lawyers who represent the most vulnerable defendants.

The Legal Aid members, whose contract ends Monday, have not set a strike deadline, said Jane Fox, a staff attorney with the agency and chair of the union.

“I’m very hopeful that we will continue our good-faith negotiations,” Ms. Fox said. “But our employer and the city should know we now have what we need if we need to move forward to call for a strike.”

While Legal Aid, a nonprofit that contracts with the city, is the dominant public defense organization in New York, several others provide similar services. Some also have contracts ending soon and will vote on whether to strike, Ms. Fox said.

The defenders’ complaints are not new. Legal Aid lawyers have said low starting salaries have forced some of them to take second jobs. In recent years, defender organizations have lost large numbers of staff.