TORONTO -- Canada is making progress in the battle against COVID-19 but will have to be extremely cautious about removing physical distancing measures and other restrictions, Prime Minister Justin Trudeau said Sunday.

"All these measures we've brought in are about helping you do the things that will get us through this – and it's working," Trudeau said at a press conference outside his home.

"We've seen the numbers trending in the right direction, so we need to keep doing what we're doing and keep being extremely careful."

As of early Sunday afternoon, Canada had seen nearly 34,000 confirmed cases of the novel coronavirus and more than 1,500 associated deaths. More than 11,000 patients are known to have recovered.

Some parts of the country have reported data that suggests their regional curves may be flattening, with case numbers declining from their peak and some provinces going days without finding a single new case of COVID-19.

Federal authorities have urged viewing that information from a "cautiously optimistic" perspective, as Chief Public Health Officer Dr. Theresa Tam said on Wednesday.

The federal government wants to see more prolonged decreases in key indicators before physical distancing measures are relaxed. This was evidenced again on Sunday, when the prime minister was asked about the approach being taken in Austria, where some non-essential stores have been allowed to reopen and others will soon be added to the list if infection numbers do not spike.

"We are listening very carefully to experts and looking very carefully at what is working and has worked in other jurisdictions, and seeing how and if that can be adapted to us," Trudeau said.

The prime minister said "many" decisions about reopening schools, businesses and public spaces will be made at the provincial and territorial level, both because it was provinces and territories that enacted them and because the different situations in different parts of the country could allow for some to lift their restrictions before others.

He said the federal government is working with provinces and territories to develop "a set of principles and approaches that can be applied at different moments and in different ways."

It has been suggested that restrictions could yo-yo between being lifted and being reenacted, based on how each adjustment affects the strain on hospitals in the area. Researchers at Harvard have found that, in the U.S. at least, this approach could last until 2022 before life fully returns to normal.

The Canadian government has been reluctant to speculate on timelines for lifting restrictions, preferring to use vague terms such as "weeks" and "months" – although in recent days, "weeks" has increasingly been the word of choice to describe when a first round of reopenings could occur.

Trudeau echoed the call for caution on Sunday, saying he does not want to see any part of the country relax too many restrictions at once and cause a new spike in cases, which could potentially put the area's health-care system at risk.

"It's not going to suddenly reopen in any part of the country, overnight, to what it was before," he said.

"We are going to have to be very, very careful, very gradual, very progressive if we are to prevent that kind of resurgence that would send us all back into lockdown."