A man in the Canadian province of Nova Scotia has shot and killed over 10 people, including at least one police officer, during a 12-hour rampage.

Police told reporters that Gabriel Wortman, 51, shot people in several locations across the province and they were still trying to establish a final death toll.

They added that Wortman was dead, but would not confirm an earlier TV report that he had been shot and killed by the Royal Canadian Mounted Police.

The killings started late on Saturday in the small Atlantic coastal town of Portapique, about 130km north of the provincial capital, Halifax.

It appeared to be the worst act of mass murder in Canada since a gunman killed 15 women in Montreal in December 1989.

"This is one of the most senseless acts of violence in our province's history," Premier Stephen McNeil told reporters.

Canadian Prime Minister Justin Trudeau, speaking to reporters in Ottawa, deplored what he called "a terrible situation".

Mass shootings are relatively rare in Canada, which has tighter gun control laws than the United States.

The worst gun incident in the country in recent years occurred in January 2017, when a man shot dead six people at an Islamic cultural centre in Quebec City.