Justin Bourque, 24, was seen in three different places around Moncton, the latest instance after daylight Thursday morning, said Royal Canadian Mounted Police Commander Marlene Snowman.
Heavily armed RCMP officers are combing streets and woods in search of Bourque, who was wearing military camouflage and carrying two rifles in a picture released by police on Twitter. Schools and government offices were closed, and the city pulled its buses off the roads. Mail delivery was suspended.
Police have commandeered armored trucks and told residents to stay indoors.
RCMP Const. Damien Theriault said police responded to a call Wednesday evening about an armed man in the north end of Moncton. Three of the responding officers were killed and two were wounded.
They were the first homicides this year in the city of 69,000 about 180 miles (290 kilometers) east of the Maine border. Theriault said the city had no homicides last year.
"We have been blessed until this point," Theriault told The Associated Press.
Police released a map of a large portion of the northwest section of the city, including a heavily wooded area, where they wanted people to remain inside with their doors locked. Families hunkered down in their basements.
Authorities warned people to expect roadblocks and traffic disruptions.
Theriault broke down in tears at a media briefing Wednesday, saying he personally knew the officers. Unable to complete his sentence, he excused himself.
The two injured officers were being treated for non life-threatening wounds.
Daniel St. Louis, a commercial photographer, said he came upon the scene around 8:30 p.m. and saw two police vehicles on different streets with blood inside.
One of the vehicles, a marked police cruiser, was surrounded by shattered glass. The other, an unmarked SUV with its lights still on and the driver's side door left open, had several bullet holes through its front windshield.
"I walked over and I saw two feet, facing the street, toes up," said St. Louis, 51. "I realized, 'Oh my God. There's somebody down.' As I got close, I realized it was an officer and this is not a good situation."
St. Louis said he doesn't know what to make of the tragedy.
"Our quiet little city, what is going on here?" he said. "How is this happening to us? It always happens to somebody else."
Danny Leblanc, 42, said he saw the shooter in the distance Wednesday evening, wearing a camouflage outfit and standing in the middle of the street with his gun pointed at police cars.
The construction worker said he believed it was an RCMP officer until he heard a burst of gunfire coming from the man's gun.
He said he quickly retreated into his home and remained there with his family. At one point a neighbor posted on social media that their kitchen window was shattered by gunfire.
Leblanc said few people on his normally quiet street were sleeping as they awaited word at midnight on whether an arrest had been made.
"It's devastating. I don't know if he was on a hunt for them, or what," he said.
Police had a number of roads in the city blocked and traffic was backed up on major arteries across the city. Drivers were asked to stay out of the area.
"It is a terrible tragedy," said Mayor George LeBlanc. "We as a city must pull together as a family to support those who have suffered losses."
Such violence is rare in Canada, particularly on the east coast.
The shootings brought back memories of when four Royal Canadian Mounted Police officers were killed in the western Canadian province of Alberta in 2005 in the deadliest attack on Canadian police officers in 120 years. They had been investigating a farm in Mayerthrope, a hamlet in Alberta, when a man shot them. The gunman was killed.
Canadian Prime Minister Stephen Harper, in Brussels for a meeting of the G-7 group of nations, offered his condolences to the families, colleagues and friends of those affected by the shootings.
Associated Press writer Rob Gillies in Toronto contributed to this report.