MONTREAL -- Quebec Premier François Legault is asking the Trudeau government to ban all international travel departing from Canada that is not essential, such as people flying to all-inclusive resorts.

He said he has already made the request privately and now Quebec is "waiting" for the federal government to make a decision.

"We are realizing there are some people who are coming back from international travel with the virus," Legault said in a press conference Tuesday.

"I don't want us to experience what we experienced after spring break in March. And I still don't undestand [how] a person decides to go to Punta Cana or to Cancun, in an all-inclusive hotel, given the situation that we're experiencing here in Quebec."

Legault also called on the federal government to enforce people's post-travel quarantine requirement more strictly, and said Quebec is ready to take extra measures on its own if Ottawa doesn't take action.

"It's not enough to have robocalls," he said.

"If we don't get an answer from the federal government, we'll see if we can put in place some measures ourselves in airports in Quebec."

Prime Minister Trudeau sounded a similar note on Tuesday, however, warning travellers that new restrictions could arrive with little notice.

During a French segment of his press conference, the prime minister urged people who have booked trips to cancel them, saying the risk of bringing home the virus is not worth it.

When asked if he foresees problems making this kind of sweeping ban, given people's rights to movement, Legault said that it's already been done to a lesser extent, such as banning incoming flights from the U.K. in order to protect Canada from the new variant of COVID-19.

He said that while it may be difficult to determine exactly what's essential, it's not always hard to see what's definitely non-essential, such as going to a resort.

"I'm sorry, but that is not essential travel, and there must be a way -- I think it's possible -- to stop these kinds of trips," he said.

"We said to the federal government [that] we're ready to dicuss how. But I feel that Quebecers are fed up, and I am as well, when I see that we're making efforts, and there are people that travel for fun abroad."

Quebec Health Minister Christian Dubé later said that there have been serious talks about how the province can crack down on its own.

"We are in discussions with the minister in charge of public security," he said, about whether Quebec can enforce the Quarantine Act -- a federal law -- with the help of Quebec police forces.

Since the Quarantine Act is federal, if the province wants to give fines under it, it must still find a way to go through the federal government, said Dubé.

Legault said that the province wants several new measures, as well as in-person enforcement on quarantines.

"What I've said is that I would like there to be a better follow-up," he said.

He'd like to see travellers not only provide a recent negative test in order to travel home, as now required by law, but to get "if possible, another test done when they arrive," and then another a week later.

He also wants, for "the people that are supposed to be quarantining, to make sure that somebody goes and knocks on their door to make sure they are home."

He said provincial services of all kinds are already overwhelmed and he would like to see a "federal government team" take charge of this enforcement.

"Obviously I would prefer if the federal government would do all of this," he said. "But given that we are not satisfied with the work that's being done in airports... we can go do a part of the work," he said, while respecting Quebec's jurisdiction.

Legault said that he's particularly worried about travellers bringing the new variants of the virus into Quebec. However, he said he's encouraged by the province's recent daily case counts, which have dropped overall in the last week.

Hospitalizations have stayed steady, so the province's health-care system remains under serious strain, with staff being trained on Quebec's COVID-19 triage protocols that will help them decide who will get lifesaving care if resources become too tight to treat everyone.

LISTEN ON CJAD 800 RADIO: "I'm asking Ottawa to ban non-essential international travel" says Legault