Thousands of New Yorkers - including mayoral candidate Christine Quinn - have marched to protest the shooting death of a gay man in the neighbourhood that was the cradle of the modern US gay rights movement.

"Homophobia's got to go," protesters chanted on Monday as they rallied waving signs to honour the memory of "the gay angel Mark Carson" and "hate no, gun control yes."

Mark Carson, 32, was killed with a bullet to the head on Friday night in Greenwich Village, allegedly by a 33-year-old man who shouted homophobic slurs at him and also threatened to kill the friend walking with him.

"You want to die tonight?" was among the cries from suspect, Elliot Morales, witnesses said.

"It is clear that the victim here was killed only because, and just because, he was thought to be gay," New York City police chief Ray Kelly said on Sunday, emphasising the victim did nothing to provoke the attacker.

The murder has sparked a strong response from New York's gay community, not least because it happened in a neighbourhood known for its tolerance and where the so-called "Stonewall riots" in 1969 sparked the modern gay rights movement.

"A lot of people thought when [same-sex] marriage laws passed in this state that everything would automatically get better, but changing people minds takes longer," said writer Marissa Higgins, 23, who wed her wife Danielle in February. "Until then, unfortunately there is going to be violence."

Same-sex marriage

More than 25 gay rights groups, including GLAAD, the New York Anti-Violence Project and the Human Rights Campaign pledged to join the rally, as did local officials, including mayoral candidate Quinn, who also heads the city council.

Quinn, 46, is gay and invited many New York celebrities to her wedding a year ago.

Monday's march ended at the site of the shooting, on the corner of 6th Avenue and 8th Street, where flowers and candles continued to be left throughout the day.

The murder came as several US states passed laws in recent weeks to legalise same sex marriage, bringing the total to 12 states and Washington, that now allow the practice. New York approved same-sex marriage in 2011.

Some have expressed concern over an increase in homophobic incidents in New York, with 22 counted so far in 2013, up from 13 during the same period last year.

Morales, the suspect in the killing, was arrested shortly after the incident and charged on Sunday.