The Taoiseach has admitted it will be "very challenging" to meet this month's vaccination targets, given the ongoing supply issues.
Micheál Martin has also indicated that the Government is against the idea of a so-called 'vaccine bonus' which would give those who are fully vaccinated greater rights to move about or mix with larger numbers of people socially.
The Government has promised that more than 1.1m vaccines will be delivered by the end of March. However, targets will not be met next week because of ongoing supply issues.
At a vaccination centre at Galway Racecourse, Mr Martin was asked directly if the March target will now be missed, given that just 84,000 people will be vaccinated next week.
The Taoiseach said all vaccination targets in the months ahead are "subject to supply", which has been problematic in recent weeks.
"But, that said, we are administering significant amounts of vaccine, even now notwithstanding the challenges we have with AstraZeneca in particular. AstraZeneca are saying that they will make up the shortfalls," he said, adding that the EU is making "additional efforts" to increase capacity and supply.
GPs have expressed concern that if the logistical issues around supply and delivery to them are not ironed out, it could put the whole rollout of the vaccine into question.
Sinn Féin leader Mary Lou McDonald said the Government's failure to communicate on the vaccine programme is denting public confidence.
"It's now very clear that there are concerns — not just about supply, but equally about the distribution of vaccines," she said.
Vaccinations of frontline healthcare workers have been impacted both this week and last week due to shortfalls in AstraZeneca deliveries.
A HSE spokeswoman was unable to say how many of these staff have yet to start their vaccinations.
“The number of frontline healthcare workers who have yet to receive a vaccine is not available, as the system is an opt-in programme where staff can self-register," she said. “The portal does not record staff who do not register for vaccination.”
Up to Tuesday, 144,581 people had been fully vaccinated, with 316,056 doses given. But it is hoped that 500,000 vaccinations will have been administered by the end of this weekend.
Regarding the potential easing of restrictions for those who have been vaccinated, Mr Martin said the European Union has decided that it will issue vaccination certs, but he said these are not vaccination passports and, at the moment, they would not provide people with greater freedom.
"Over time, whether it evolves into something greater than that remains to be seen," he said.
Asked about the opening of Cork's City Hall vaccination hub, Mr Martin said the 37 centres across the country will be used to a "far greater extent" from April onwards.
Meanwhile, people will be able to get Covid-19 vaccinations in local pharmacies from early April, according to the Irish Pharmacy Union.
IPU secretary general Darragh O’Loughlin said the move will bring relief to those who live far from the mass vaccination centres.
He acknowledged the delay is hard for the public.
“We are still a couple of weeks away, it will be into April," he said.
“Pharmacists are frustrated they are not yet involved. We know this is because of a supply issue. There has not been a reliable supply of AstraZeneca into the country so far.”