Retired General Rick Hillier says the idea that a majority of COVID-19 vaccines in Ontario are sitting in freezers is incorrect and that the province has the opposite problem.

"The information is misleading. We're actually going to run out of vaccines," Hillier told CTV Morning Live in Ottawa on Wednesday.

"Yesterday, we vaccinated more than 10,000 people in the province of Ontario. We will do the same and more again today. We are at the point now where we will start running out of vaccines as the people who need the second shot start coming back," he said.

The retired Canadian Armed Forces General is leading Ontario's vaccine distribution task force. He suggested on Tuesday that holding back 35,000 doses of the Pfizer-BioNTech vaccine contributed to the slow roll out, and acknowledged that pausing vaccinations during Christmas was a mistake.

However, on Wednesday morning, he stressed that the supply of doses in the province is dwindling rapidly.

"One hospital will run out tomorrow, another said to me last night they'll run out by Tuesday and others are saying 'should we slow down?' and the answer is no," Hillier said, "vaccinate as many people as quickly as you can and run out, and we're going to push for more vaccines to come to the province of Ontario."

According to data from the Ontario government, 60,380 doses of COVID-19 vaccines have been administered in the province as of 8 p.m. Jan. 5. There are 860 people in Ontario who have received both doses and completed their vaccinations so far.

Hillier said he expects another shipment of vaccines from the federal government next week, but he doesn't know when it will arrive.

"We don't know when it's supposed to come. We're assuming one will come and hopefully it will. We don’t know which day it will arrive but we're going to run out of vaccinations next week," he reiterated.

Ontario Liberal Leader Steven Del Duca is calling on Premier Doug Ford to bring in the military to aid in vaccine distribution and speed up the rate at which people are vaccinated.

Hillier says, however, that the issue is not one of logistics, but of supply.

"We've got 19 vaccination sites running in the province right now. We're going to ramp up to 21, 22 in the coming weeks, but the problem is there's no sense in ramping up if we don't have vaccines to go to the sites and put in people's arms," he said.

"People have to go realize the number of vaccines flowing to Canada and therefore flowing to Ontario is actually really, really small. And when you get people now coming back for their second needle to complete the vaccination program, that starts to take up an increasing proportion of what vaccines we get and it makes our flexibility even less, even tighter. What we need is more vaccines. We are working to that end. As soon as we get them, they're going to flow across the province."

1.2 million additional vaccine doses are expected to arrive in Canada this month. Prime Minister Justin Trudeau said Tuesday that he would be speaking with premiers this week to urge them to speed up their vaccination programs.

“Now is the time, with the new year upon us, to really accelerate and that's certainly what I'll be talking with the premiers about… how the federal government can support and help in getting these vaccines even more quickly out to Canadians,” Trudeau said.