NEW YORK » Police chased a man wielding a meat cleaver through midtown Manhattan today, then shot him on a crowded street after he hacked the face of an off-duty police detective who tried to tackle him, authorities said.

The man with the knife was shot at least twice and was hospitalized in critical but stable condition, police said. The detective, who had been heading home in street clothes when he intervened in the chase, was being treated at the hospital for a six-inch gash from his temple to his jaw.

“I want to commend them on their bravery,” Police Commissioner William Bratton said of the officers involved.

Police fired 18 shots at the man, but Bratton, who is retiring Friday, said he believed officers acted appropriately.

“We have a character running down the street, waving a cleaver,” he said.

The chase began on Broadway and ended about a block from Macy’s department store and Madison Square Garden, just as rush hour was getting underway.

The confrontation started, police said, when two uniformed officers encountered the man trying to remove an immobilizing boot from a parked vehicle.

Police said the suspect, Akram Joudeh, 32, had a previous address in Queens but appeared to have been living in the car.

After the officers approached, Joudeh pulled an 11-inch knife and ran, police said. A growing group of officers chased him, and at one point shot him with a Taser, with no apparent effect.

A bystander, Jonathan Schneier, said when he left work to get coffee he saw a balding man holding a cleaver, surrounded by a small group of officers yelling at him to drop the knife.

“I give credit to the police officers. They gave him many opportunities,” Schneier said. He said the man with the knife “did not look very stable.”

The man turned and ran, Schneier said.

Officers chased him down the street. An off-duty police detective tried to tackle the man, who lashed out with the knife, said the department’s top chief, James O’Neill. That’s when officers opened fire, he said.

“They shot until the threat was stopped,” said O’Neill, who is succeeding Bratton as commissioner.

Corey Melton, a photographer, was checking his phone on the street corner when he heard “a series of gunshots go off.”

Photos he took show a gray, four-door sedan with bullet holes in the windshield. His photos also show a man sitting on the ground handcuffed behind the car.

Officials said Joudeh has been arrested more than a dozen times in recent years, mostly for minor crimes, but didn’t provide details.

Attempts to locate any relatives Joudeh might have in New York were not immediately successful. It is likely to be many hours, if not days, before a lawyer is appointed to represent him.