"We pray everything we are hearing is true and that these officers will be OK in the long run," de Blasio said.
The shootout between Mozdir and a fugitive apprehension task force happened just after 1 p.m. in the West Village not far from New York University in a highly trafficked tourist area bounded by jazz clubs, restaurants a subway station and basketball court.
"It was shocking and out-of-place," said Edoardo Gelardin, 24, who was heading to lunch shortly after the shooting when he saw officers loading the victims into ambulances and officers with assault weapons sealing off the scene. "It was a little overwhelming to see a scene like that."
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.
He had also been charged with attempting to dissuade a witness from prosecution, 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 San Diego County Public Defender's Office, which represented Mozdir in the child molestation case, didn't immediately return a message seeking comment.
The fugitive task force seeks absconders from other states, Bratton said. Mozdir's weapon was recovered, authorities said.
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.