ALBUQUERQUE, N.M. — A federal judge said Thursday that New Mexico has made “undeniable progress” in addressing concerns that have lingered for decades about timely access to certain welfare benefits for some of the state’s most vulnerable residents.

U.S. District Judge Kenneth Gonzales took testimony during a daylong hearing on the findings of a special master who spent the last year reviewing the inner workings of the state’s Human Services Department and how applications are processed for emergency food aid and health coverage under Medicaid.

The hearing was part of an ongoing legal battle over whether the agency is meeting numerous court orders along with a consent decree related to a backlog of assistance claims.

Gonzales has yet to adopt the special master’s report. It could be at least two weeks before he makes a ruling.

The report raised concerns about a lack of accountability at all levels and stated that the agency lacks sufficient knowledge, skills and abilities to oversee the program.

The special master, Lawrence Parker, reiterated his concerns during the hearing, saying the state still has much work to do.

“I’ve come to the conclusion that clients haven’t been properly served in New Mexico,” he said, while acknowledging that progress has been made to address backlogs for food assistance and that timeliness has improved for processing new applications.

The New Mexico Center on Law and Poverty, an advocacy group, contends the department develops a backlog of unprocessed cases each month and that phone calls from benefit recipients often go unanswered.

Lawyers for the group complained that the problems are systemic. They accused the state of failing to meet federal timeliness requirements and of providing inadequate notices to applicants.

Both sides presented spreadsheets that included an array of data on benefit renewals and denials.

“While statistics are important, what we’re really talking about is people,” the judge said.

Gonzales visited three public assistance offices last year to get a firsthand look at the process. He also invited a number of the agency’s regional and county managers to Thursday’s hearing. He recognized them for the work they have done.

He said he heard from workers about their frustrations over a lack of training and computer problems.

When asked about the reason for the progress made in recent months, Human Services Secretary Brent Earnest said strategic investments were made but that it was a reflection of the personnel.

Earnest and other officials dismissed calls for some high-level managers to be removed, saying a shake-up would be counterproductive.

Parker told the court he stands by his recommendation to remove some employees. He pointed to Texas, Florida, Illinois and Delaware, saying other states have been able to turn struggling programs around by making changes within the administration.

He also recommended improving worker training.

The case stems from a lawsuit filed nearly 30 years ago on behalf of a single mother who ran into a bureaucratic wall while trying to obtain assistance for herself and her son after her wages were cut drastically.

In 2016, the judge held Earnest in contempt over allegations that he did not diligently attempt to comply with court orders concerning the handling of Medicaid benefit renewals, eligibility for immigrants, training for agency employees and other administrative requirements.

Later that same year, the judge appointed the special master as an alternative to a more far-reaching request by advocates for aid recipients that a federal receiver implement administrative changes.

The calls for outside oversight followed testimony by state caseworkers that expedited food aid applications were falsified to meet federal deadlines — sometimes under pressure from management — likely delaying the delivery of benefits as a result.

Both the state and the plaintiffs indicated to the judge they want to work on a path forward, with the plaintiffs arguing that adopting the special master’s report would mark the first step as it calls for the provisions of the consent decree to be revisited.

Attorneys for the agency said they agree with many of the report’s recommendations but argued that the decree was never intended to be permanent. Barring any violations of federal law, they said the court should have no interest in micromanaging a state agency.