As infections fuelled by the Omicron variant threaten to overwhelm Canada's health system, Prime Minister Justin Trudeau is promising the provinces will have enough COVID-19 vaccines to provide everyone eligible booster shots and fourth doses if they become necessary.

Trudeau made the pledge in a statement issued late Monday after he spoke with provincial and territorial leaders, saying Ottawa will do all it can to help them cope with the fifth wave of the pandemic.

"(The premiers) expressed concern over the strain on health-care systems, businesses, workers and families across the country," the statement said. "They raised the need to strengthen health-care systems, noting the particular challenges with health human resources capacity."

The federal government has said provinces and territories will receive a combined 140 million rapid tests this month, although the statement did not provide details on when the deliveries will be scheduled.

Meanwhile, hospitalizations related to COVID-19 continued to surge throughout Canada on Tuesday.

Quebec reported an all-time high of 2,742 hospitalizations, 255 of whom were in intensive care, while Ontario reported 3,220 hospitalizations, with 477 patients in the ICU and 250 COVID-19 patients on ventilators.

On Monday, Quebec's director of public health, Dr. Horacio Arruda, tendered his resignation, citing an erosion in public confidence in health-protection measures.

In recent weeks, the province has reinstated several stringent health measures including a curfew for the second year in a row. As well, the province has reported 12,028 deaths since the beginning of the pandemic — a per-capita death rate that is almost double that of Ontario.

Meanwhile, the provinces recorded a combined total of 20,279 new COVID cases on Monday, although the actual number is likely much higher due to a lack of access to testing.

In Alberta, the chief medical officer of health, Deena Hinshaw, said the active case count released Monday by the provincial government — 57,000 — is probably 10 times lower than the actual number.

"It's my belief that we need to prepare for a significant impact (to the health system) at this point given the cases we've seen," Hinshaw said, adding that only high-risk cases are now eligible for PCR tests, including continuing care residents and front-line health-care workers.

The rapid spread of Omicron across the country has prompted the U.S. Centers for Disease Control and Prevention to advise Americans to avoid travelling to Canada.

In Ontario, Premier Doug Ford confirmed students will return to school classrooms on Jan. 17. The schools were shut last week as the government enacted other public health measures amid growing strain on the province's health system and pandemic-related staff shortages across essential workforces.

The government said promised shipments of N95 masks were sent to all school boards and school authorities as of Monday, while some shipments to child-care centres were still to go out this week. As well, the province is accelerating boosters for education workers and installing more HEPA air filters.

Schools reopened across British Columbia and Alberta on Monday with slightly higher absence rates among students and teachers in some districts after a prolonged Christmas break.