Before opening fire early Saturday, the gunman confronted the victim and his companion in Greenwich Village and asked if they "want to die here," Police Commissioner Raymond Kelly said.
The shooting follows a series of recent bias attacks on gay men in New York, but this was the first deadly one.
About 15 minutes before the bloodshed, the gunman was seen urinating outside an upscale restaurant a few blocks from the Stonewall Inn, a birthplace of the gay rights movement, according to Kelly. He then went inside the restaurant and asked if someone was going to call the police about him.
Police said the gunman, identified later as 33-year-old Elliot Morales, told both the bartender and the manager, "if you do call the police, I'll shoot you" and opened his sweatshirt to reveal a shoulder holster with a revolver and made anti-gay remarks, Kelly said.
Morales has a previous arrest for attempted murder in 1998, police said. Details of that arrest weren't immediately clear.
Out on the street minutes later, the gunman and two others approached the 32-year-old victim, identified by police as Harlem resident Marc Carson, and a companion on Sixth Avenue. One of the three men yelled out, "What are you, gay wrestlers?" according to Kelly.
The two men stopped, turned and, according to Kelly, said to the group taunting them, "What did you say?" - then kept walking.
"There were no words that would aggravate the situation spoken by the victims here," the commissioner said. "This fully looks to be a hate crime, a bias crime."
Two of the men kept following the victim and his companion, Kelly said, adding that witnesses saw the pair approach from behind while repeating anti-gay slurs.
The gunman asked the men if they were together and when he got an affirmative answer, Kelly said, "we believe that the perpetrator says to the victim, 'Do you want to die here?'"
That's when suspect produced the revolver and fired one shot into Carson's cheek, Kelly said.
The gunman fled to 3rd Street, where an officer who had heard a description on his radio spotted him and ordered him to stop, Kelly said. The suspected gunman threw his revolver to the ground and was arrested on the edge of the New York University campus.
Police found the mortally wounded victim on the pavement. He was pronounced dead at Beth Israel Hospital.
Authorities said they could not immediately identify Morales because he was carrying forged identification. But investigators learned his name after the forged ID was submitted to the department's Facial Recognition Unit.
Of the other recent New York bias attacks on gay men, one was reported last week on nearby Christopher Street, where a 35-year-old man told police he was beaten up and heard anti-gay words after leaving a bar.
On May 10, two men trying to enter a billiards hall on West 32nd Street were approached and beaten by a group shouting homophobic slurs, police said.
And on May 5, a man and his partner were beaten near Madison Square Garden after a group of men wearing Knicks shirts hurled anti-gay slurs at them.
The commissioner said Saturday that police were looking into possible links between the incidents.
Multiple lawmakers have condemned the violence.
"I am horrified to learn that last night, a gay man was murdered in my district after being chased out of a Greenwich Village restaurant and assailed by homophobic slurs," New York City Council Speaker Christine Quinn said. "I stand with all New Yorkers in condemning this attack."
The Democratic mayoral candidate said there was a time in New York when hate crimes were common - when two people of the same gender could not walk down the street arm in arm without fear of violence and harassment.
But "we refuse to go back to that time," she said. "This kind of shocking and senseless violence, so deeply rooted in hate, has no place in a city whose greatest strength will always be its diversity."
New York State Sen. Brad Hoylman, a Democrat whose district includes Manhattan's West Side, called on New Yorkers "to unite against hate and gun violence."
And State Assemblywoman Deborah Glick declared that "New York is not open for bigotry."
The New York City Anti-Violence Project plans to gather on Friday night for what it calls a "Community Safety Night."