Police previously said Edwards had links to Mayfair and Havelock North, is a drug user and is considered dangerous.
There is a warrant for his arrest.
The vehicle used during the incident has been recovered by police.
On Monday morning a group of contractors had been waiting in their van at the Gull service station when a woman suddenly appeared, asking them to take her to the police station as her partner was going to beat her up.
Moments later a man, understood to be the distressed woman's partner, appeared at the side of the vehicle but Agworks van driver Lisa Mulligan drove away.
Ms Mulligan said the man chased them down the road in his own vehicle, ramming their white van up to 12 times.
The pursuit came to an end at the intersection of Grays Rd and Heretaunga St West, where another occupant of the van said the man "manoeuvred" them into the roundabout before ramming them while they were stationary.
A witness said the man then tried to climb into the van and grab the woman.
After the Grays Rd resident threatened to call the police, the man got back in his vehicle, rammed the van a further three times and then drove off after apparently aiming for her, too.
Four people were taken to Hawke's Bay Hospital, with two discharged later that day.
The other two victims - a male in his 20s and female in her 30s - were being supported by their families, police and Victim Support staff.
Police confirmed the incident was domestic-related and that the offender and the victim were known to each other.
The Serious Crash Unit completed a scene investigation and further inquiries were being made, a police spokesperson said.
Anyone with information as to Edwards' whereabouts is asked to contact the police or provide information anonymously via Crimestoppers on 0800 555 111.