Canada Prime Minister Justin Trudeau has tested positive for COVID-19 but is “feeling fine” and will continue to work remotely from home.

Mr Trudeau said two of his children also had the virus and a test on Monday revealed he had been infected as well.

He used a televised virtual press conference to denounce anti-vaccine protesters who filled Canada’s capital to complain about restrictions.

“Canadians were shocked and quite frankly disgusted by the behaviour displayed by some people in our nation’s capital,” Mr Trudeau said.

“I want to be clear. We are not intimated by those who hurl insults and abuse at small businesses and steal from the homeless. We won’t give in those who fly racist flags. We won’t cave to those who engage in vandalism or dishonour the memory of our veterans.”

Some demonstrators travelled in truck convoys and parked on the streets around Parliament Hill, blocking traffic – and a smaller but significant number remained on Monday (local time).

Many Canadians were outraged by images at the weekend of some protesters urinating on the National War Memorial and dancing on the Tomb of the Unknown Soldier, while some carried signs and flags with swastikas.

Many refused to wear masks in hotels, malls and supermarkets and one homeless shelter reported protesters had demanded it feed them.

Canada has one of the world’s highest rates of vaccination against the coronavirus – shots that are primarily designed to keep those who become infected from falling seriously ill.

Protest organisers have called for the elimination of all restrictions and vaccine mandates and Mr Trudeau’s removal, though he is responsible for very few of the restrictions. Most were put in place by provincial governments.

The Ottawa police department has said it is investigating possible criminal charges over some actions during the protests.

“To those responsible for this behaviour, it needs to stop. To anyone who joined the convoy but is rightly uncomfortable with the symbol of hatred and division on display, join with your fellow Canadians, be courageous and speak out. Do not stand for or with intolerance and hate,” Mr Trudeau said.

Some were protesting a rule that took effect on January 15 requiring truckers entering Canada to be fully immunised.

The US has imposed the same requirement on truckers entering that country so Canada removing it would make little difference.

Some opposition Conservative politicians served coffee to the protesters and Conservative party leader Erin O’Toole met some protesting truckers.

The demonstration also attracted support from former US president Donald Trump.

-AAP