Law enforcement sources told CNN that the suspect had possible explosive devices strapped to his body and in his vehicle, but a U.S. official said later that no explosives were found.
At least nine officers were involved in the shootout, Mina said. Several coroner vans were seen traveling toward the nightclub.
One officer suffered an eye injury when a bullet struck his Kevlar helmet, said Danny Banks, special agent in charge of the Florida Department of Law Enforcement's Orlando bureau. The helmet saved the officer's life, Banks said.
The shooter is not from the Orlando area, Mina said. He has been identified as Omar Saddiqui Mateen, 29, of Fort Pierce, about 120 miles southeast of Orlando, two law enforcement officials tell CNN.
Orlando authorities said they consider the violence an act of domestic terror. The FBI is involved. While investigators are exploring all angles, they "have suggestions the individual has leanings towards (Islamic terrorism), but right now we can't say definitely," said Ron Hopper, assistant special agent in charge of the FBI's Orlando bureau.
Authorities are also looking into the possibility the attack was a hate crime, a law enforcement source told CNN.
The shooting began around 2 a.m., and an officer who was working at the club responded, Mina said. The officer engaged in a shootout outside the club, after which the gunman ran into the club.
"That turned into a hostage situation," Mina said.
Authorities were getting calls from people inside the club but away from the gunman, the chief said.