TORONTO -- Some pharmacies in Ontario say they are already starting to run short on doses of AstraZeneca’s COVID-19 vaccine less than a week after the province launched a pilot project to roll out the shots.

Loblaw said pharmacists at Shoppers Drug Mart and Loblaw pharmacies in Toronto, Kingston and Windsor-Essex have vaccinated more than 28,000 Ontarians so far as part of the pilot, but some locations have already run out of supply.

“While some stores have run out, others expect to be through the limited supply in the coming days,” the company said in a statement Monday. “We continue to see a high demand at these participating pharmacies, demonstrating the important role that pharmacists play in delivering convenient and accessible healthcare to Ontarians.”

Ontario launched the pilot program on Thursday to roll out the vaccine at hundreds of pharmacies in three health units.

The vaccine is easier to store and transport, making it ideal for distribution through pharmacies and doctors’ offices. Because there is insufficient data about how well it functions in people over 65, Ontario is only administering it to those who are or have been 64 years old and under this year.

After the pilot launched last week, pharmacies in the three health units were inundated with people lining up and phoning to try book appointments to get vaccinated. There was also some initial confusion about who is eligible to receive the shot at a pharmacy.

The federal government authorized AstraZeneca’s COVID-19 vaccine for use in Canada on Feb. 26.

Ontario has since received 194,500 doses of the vaccine manufactured by the Serum Institute of India.

However the federal government’s website says a schedule for further deliveries of the vaccine is yet to be determined.

Speaking with CP24 Monday night, Minister of Public Services and Procurement Anita Anand didn’t provide a specific delivery schedule, but said millions of doses will arrive in the second and third quarters of the year.

“We'll be getting 20 million doses of AstraZeneca from the United States over the second quarter --  that's just before the month of June ends -- and over the third quarter prior to the end of September.”

About 500,000 of the 2 million doses ordered from the Serum Institute of India have already arrived in the country, Anand said.

As pharmacies say they are running out of supply, a senior government source told CTV News Monday that Canada’s vaccine advisory committee is set to recommend that the AstraZeneca vaccine also be given to those 65 years old and over.

Ontario Solicitor-General Sylvia Jones told CP24 that while Ontario will look at the new guidance, the province has no plans to expand the use of AstraZeneca to older people while the supply remains low.

“As those inventories increase, as we receive more vaccines, we will absolutely be able to lower the age frame and also expand more pharmacies and give more vaccines to primary health care practitioners,” Jones said.

While the federal government’s website does indicate that Ontario is expected to receive hundreds of thousands of doses of the Pfizer-BioNTech vaccine each week through May, those doses are destined for hospitals and mass vaccination sites where people 80 years old and over are being vaccinated, along with other priority populations.

While some countries have paused their use of the AstraZeneca vaccine over concerns about a possible link to blood clots, Health Canada has said there is no evidence to link the vaccine to the clots so far and the federal government has said there have been no cases in Canada.