The wounded officers were in stable condition, Police Commissioner William Bratton and Mayor Bill de Blasio told reporters.
"We pray everything we are hearing is true and that these officers will be OK in the long run," de Blasio said. The law enforcement officials' exact injuries were unclear.
The suspect was identified by federal and police officials as Charles Richard Mozdir, who was wanted in a California case. His weapon had been recovered, the mayor and commissioner said.
The shooting happened just after 1 p.m. in the West Village not far from New York University when a fugitive apprehension task force tried to serve a warrant to Mozdir, who was inside a smoke shop just north of a busy subway station.
A $1 million bench warrant was issued for Mozdir's arrest on June 15, 2012, after he skipped an arraignment in San Diego Superior Court on child sexual assault charges, according to Steve Walker, a spokesman for the San Diego County district attorney. He had posted $250,000 bail.
Mozdir was wanted on five counts of lewd acts upon a child younger than 14 and a charge of attempting to keep a witness from prosecuting a crime, according to the criminal complaint.
His case had recently been featured on CNN's "The Hunt with John Walsh." Mozdir was accused of abusing a young boy while babysitting him and authorities later found evidence of child pornography and bestiality on his cellphone and computers, according to the show's website, quoting federal authorities.
Authorities have searched for him in Coronado, Georgia, California and Mexico, according to the show.
The fugitive task force seeks absconders from other states, Bratton said. He declined to comment to reporters at the scene Monday.
The violence recalled a deadly shootout that left a gunman and two auxiliary New York City police officers dead on another Greenwich Village street in March 2007.
That gunman, David Garvin, killed a bartender, according to police, and then turned crowded streets packed with storied taverns into a shooting gallery. Unarmed volunteer officers Eugene Marshalik and Nicholas Todd Pekearo were killed.
Associated Press reporter Jennifer Peltz contributed to this report.
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