NEW YORK — Two police officers were shot and wounded by a gunman they encountered in the stairwell of a public housing project they were patrolling, and the gunman later killed himself, authorities said.

Police said three officers were on the sixth floor of the Melrose Houses complex in the Bronx Thursday night when they encountered two people. One person pulled a gun and opened fire, hitting one officer in the face and the other in the abdomen, before running into an apartment on the seventh floor. The third officer was not hurt.

Officers responding to the scene found the gunman in the apartment dead of an apparently self-inflicted gunshot wound. A handgun and a shotgun were found inside the apartment, police said.

The second person who encountered the officers in the stairwell was taken into custody, and three people in the apartment were being questioned, said New York Police Department First Deputy Commissioner Ben Tucker.

The shooting happened about 5 miles from where Mayor Bill de Blasio was delivering his State of the City address, much of which was dedicated to praising the work of police officers.

De Blasio, a Democrat, was told about the shooting as he finished his speech and left the stage. He met with the family of one of the officers at the hospital where they were being treated.

“Our brave officers were doing their jobs tonight in our public housing on patrol keeping residents safe,” de Blasio said. “Both officers are alert and communicating, and we are praying for the best here.”

One of the officers is a 29-year-old man, and the other is a 24-year-old woman, said Robert Boyce, the police department’s chief of detectives. The officers, who are assigned to the Housing Bureau, have been on the force for about two years. Police would not provide the names of the officers or the person who was in custody.

The officers were shot while they were conducting a vertical patrol, where officers start in the lobby of a public housing project and walk the stairwells up to the roof and back down, Tucker said.

The head of the police officers’ union, Patrick Lynch, said the shooting shows the dangerous nature of the job.

“We need your support to teach our young folks that pulling a gun on a police officer works for no one,” he said. “This goes to show the dangers police officers face each and every day.”