Tam made her remarks days after the provinces of Ontario and Quebec - which together account for around 61% of Canada's population of 38.5 million - said they were more optimistic about their ability to deal with coronavirus infections.
"There are early indications that infections may have peaked at the national level," Tam said, noting daily case counts had dropped 28% compared to the previous week.
"However, daily hospital and intensive care unit numbers are still rising steeply, and many hospitals across Canada are under intense strain," she said in a news briefing.
Over the past week, an average of more than 10,000 people with COVID-19 were being treated in hospitals every day, surpassing peak daily numbers for all previous waves, she said.
Although politicians at all levels have repeatedly urged Canadians to get inoculated against the virus, Tam said 6.5 million people in the country were still not fully vaccinated.
(Reporting by David Ljunggren in Ottawa and Ismail Shakil in BengaluruEditing by Paul Simao)