Officials say Justin Bourque, 24, was spotted multiple times early on Thursday morning.
They have warned people to stay inside and lock their doors.
The two wounded Royal Canadian Mounted Police (RCMP) officers are undergoing surgery in hospital and their conditions remain unknown.
“We have an armed and dangerous individual and we do not know where he is,” RCMP Commanding Officer Roger Brown told reporters, asking citizens to remain “vigilant”.
RCMP Supt. Marlene Snowman warned that the suspect was armed with high-powered firearms.
“He’s not known to us, he’s a young person,” she said.
“We’re doing a complete investigation to learn as much as we can about him, about his history, what may have sparked this.”
New Brunswick Premier David Alward said he felt “incredible grief” stemming from the incident.
The officers were shot while responding to a report of an armed man at the north-west side of the town at about 20:00 local time on Wednesday,
Police established road blocks in an effort to seal a perimeter around the residential area and combed nearby woods, searching through the night and into the morning.
Schools in the town are closed, buses are not running, and postal service has been suspended.
Pedestrians and motorists have been asked to stay away from the area.
Justin Bourque was spotted after daylight, but Marlene Snowman warned he was “very mobile”.
“There’s no question that we’re going to continue this search in order to apprehend him,” she said.
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