MONTREAL -- The Quebec government defended its COVID-19 vaccination program on Wednesday, saying the federal government must do more to get doses to the province.

Just under 40,000 people in Quebec have been vaccinated thus far and Health Minister Christian Dube said the only thing holding things up is a lack of supply.

“Not only can we vaccinate, but we can vaccinate more,” he said.

Dube pointed to data from the previous day, when over 6,000 people received the first dose of the vaccine, saying the province has “not yet reached our cruising speed.”

Premier Francois Legault said the province has been promised 230,000 doses by the end of January but said there is a capability of administering that many in a single week.

“We could be vaccinating four times more people than we do right now, but we don't have enough doses,” he said.

Dube tied the extended lockdown measures announced the same day to the province's vaccination effort, saying the goal is to have 250,000 people vaccinated by the hopeful end-date of Feb. 8. That would inclue all people living in Quebec's CHSLDs and the majority of healthcare workers, as well as workers in private retirement homes.

Public health chief Horacio Arruda defend the province's revised plan of holding back booster doses from those who have received the first shot. A spokesperson for Pfizer, maker of the first vaccine approved for use against COVID-19 in Canada, told CTV News that the company does not support Quebec's plan.

Arruda said people would eventually receive the second dose on a “modified calendar.”

“In Quebec, we've already done work on what we call modified calendars, with what the companies recommend,” he said. “We believe protecting as many people in the short term will save lives. In a context of public health in a pandemic, we're not in a normal situation.”

Family members of residents living in the Maimonides long-term care home, which was one of the first places where the vaccines were administered in Quebec, threatened to take legal action against the provincial government if they follow through on their plan to hold back second doses.