One of New York City’s biggest and most important rental aid programs has been “plagued with problems” that make it harder for people to leave the city’s overburdened homeless shelters and find permanent homes, according to a state audit report released Thursday.

Based on a sampling of cases, the audit found “systemic irregularities” in the administration of the program, which provides vouchers that allow tenants to put 30 percent of their income toward rent while the city pays the rest.

Landlords did not receive aid payments on time, and some people in shelters faced “numerous delays” in getting the documentation they needed to look for apartments, while others were inaccurately classified as having left the shelter system, according to the report, which was conducted by the New York State comptroller’s office.

The comptroller, Thomas P. DiNapoli, said households waited 10 months on average to be found eligible for the program, known as the City Fighting Homelessness and Eviction Prevention Supplement, or CityFHEPS. It is not the same as a federal Section 8 voucher, but it works in a similar way.

The city’s Department of Social Services, which runs the rental aid program, should “improve its management,” Mr. DiNapoli said in a statement. He noted that with New York facing a housing affordability crisis, the city needs “an effective and efficient rental assistance program.”

City officials pushed back on Mr. DiNapoli’s findings, characterizing the reported problems as anomalies. They said in the fiscal year ending in June, the city had helped more than 13,000 households secure apartments using the voucher program, up from about 7,000 three years ago.