Advocates and others here have protested the Police Department’s 23 shootings by officers since 2010 — 18 of them fatal — with some people calling for the police chief’s resignation and for a Justice Department investigation.

Albuquerque, the largest city in New Mexico with a population of 546,000, has 1,100 sworn officers. New York City, with a population of 8.4 million and a uniformed police force of 35,000, had 22 fatal shootings by officers in the same time period.

The police union payments were reported on Friday by The Albuquerque Journal. Twenty Albuquerque officers involved in shootings in 2010 and 2011 were paid by the union, with 16 receiving $500, two $300, one $800 and another $1,000, the newspaper reported, citing internal union financial documents. Many of the officers who received the money were involved in the 15 fatal shootings in Albuquerque during that time.

Executives of the union, the Albuquerque Police Officers’ Association, said the payments had been given to officers after the shootings and that the practice had gone on for at least two decades. They said the payments of up to $500 were to cover the costs of out-of-town trips for officers and their families after stressful episodes, and that any payment to an officer beyond $500 was for other union-related matters. The executives denied that the money was intended to reward officers who fired their weapons.

“It’s difficult for people to understand what officers involved in shootings go through — the self-doubt, the worry — and we take great offense to the fact that people are referring to this as a reward system,” the union’s president, Joey Sigala, said in an interview. “We hold onto the honor and the integrity of this profession. And we take great pride in this community.”