France at the weekend begun a third nationwide lockdown, this one lasting four weeks, and its hospital system remains under pressure.

The number of people being treated in intensive care units for coronavirus is at the highest point in France in almost a year - more than 5600 cases.

France is hoping a ramp up of its vaccination campaign, combined with the one-month lockdown, will help it regain control over the latest outbreak.

On Tuesday the country started administering shots of the COVID-19 vaccine inside the Stade de France, the stadium that once hosted soccer's World Cup final.

France is, however, on track to reach the milestone of 10 million first doses earlier than the mid-April target it had set.

Across the Atlantic, Canadian Prime Minister Justin Trudeau said the virus variants fuelling the latest global coronavirus surge are also spreading in his country.

"Around the world, countries are facing a very serious third wave of this pandemic," Trudeau told a news conference on Tuesday.

"And right now, so is Canada."

Canada has averaged nearly 5,200 new coronavirus cases per day over the past week, and has recorded a total of more than a million positive tests and 23,000 deaths.

The Canadian province of Ontario - the nation's most populous - entered a limited lockdown on Saturday, but some local health officials are calling for more drastic measures.

Trudeau said he would speak with Ontario Premier Doug Ford later on Tuesday, without providing further details.

At a separate briefing on Tuesday, Ford said more restrictions were coming.

"We're going to have further restrictions moving forward very, very quickly," Ford told reporters in Toronto. "We'll discuss that tomorrow."

He expressed frustration at seeing people in Toronto allegedly "going into the mall, doing their little wander around, and coming out with no bags".

"That tells me they were just out for a daily jaunt. You can't do that."

Canadian provinces from Quebec westward to British Columbia, with the exception of Manitoba, are struggling against surging numbers of coronavirus infections.

The federal government has delivered more than 10 million doses of coronavirus vaccines so far, and provincial health agencies are in the process of administering shots.

Trudeau has said everyone among the 38 million Canadians who want to be vaccinated will be by the end of September.

Meanwhile, Austria and Hungary have set goals for when they will lift their lockdowns as vaccine rollouts take effect.

Austria is preparing to reopen up many sectors of public life in May as it emerges from the worst of the pandemic.

And some of Hungary's businesses will begin reopening as it has now given more than a quarter of its 10 million people a first vaccine shot, Prime Minister Viktor Orban said on.

Orban is trying to tame the world's deadliest COVID-19 surge and balance that with the need to reopen the economy to avoid a second year of deep recession.

"Today we reached an important milestone," Orban said.

"For a year we have lived our lives among restrictions, curfews and personal loss.

"From tomorrow on, shops can reopen and services can restart. There will still be pandemic rules, please respect them."

Hungary has had the highest weekly per capita fatalities in the world for several weeks, according to Johns Hopkins University data.

There were about 12,000 coronavirus patients in hospital on Monday, more than 1400 of them on ventilators, the government said.

Australian Associated Press