Mr Beard says the officer was shaken by the incident and he says he's been getting support from police and family.
He says around 20 officers are trying to locate the pair, and want to hear from anyone who's seen them.
The Weekend Herald has learned Murray Toleafoa threatened to kill the woman in 2006 after she locked him out of her West Auckland home.
But because she was so terrified of him, she would not give evidence in court and the charges were dismissed.
Police say Toleafoa fired a pistol at a constable on patrol at 1am yesterday.
The injured constable described the gun as being similar to a police-issue Glock.
The car was found abandoned in Mt Eden about an hour later, but efforts to track the pair using dogs were unsuccessful. It is believed Toleafoa and Ball fled on foot.
Mr Beard said a holster found in the car had been taken for forensic testing.
"We will continue to search for them until we find them. And we will find them.
"We do not want this search to end tragically for anyone. The best thing Mr Toleafoa can do is give himself up to police."
In 2006 Toleafoa was arrested after an incident at his then-girlfriend's house in West Auckland.
He was charged with injuring with intent, burglary, using a firearm and threatening to kill, but was not convicted as she was too "terrified" to testify against him.
A source said Toleafoa held a powerful air pistol to her head and said he would kill her.
"He obviously has a propensity for violence," the source said. "The girlfriend was terrified of him. She moved a couple of times but he found her. He told her he'd always find her.
"He is a pretty dangerous guy. He was doing standovers for gangs."
The woman did not turn up to court and Toleafoa was discharged.
Yesterday, a warrant was issued for his arrest on a charge of using a firearm against an enforcement officer.
More than 20 officers including armed offender squad members were working on the investigation.
Mr Beard said Toleafoa should not be approached. If anyone saw him they should call 111 immediately.
