Stephen Donnelly has said he expects most of the 30,000 people who had their vaccine appointments cancelled this week to receive their jab this month.
Thousands of people with underlying conditions will no longer receive their first shot of the vaccine this week after the suspension of the use of the AstraZeneca vaccine in Ireland.
However, the Minister for Health said that this group will be rescheduled this month without anyone else being delayed.
And Mr Donnelly stressed that the government is expecting a quick and positive response from the European Medicines Agency as the safety of the AstraZeneca jab is analysed.
He told Morning Ireland on RTE Radio One: "If the EMA comes back, as we hope they will, with a very positive report later in the week, then it will be a very short period to reschedule.
"What we've done is build a vaccine system with the capacity to administer more vaccines than we have in, so hopefully the 30,000 for this week will be rescheduled very quickly. Will everybody be done by the time left in March? I'd say pretty close, maybe there'll be a little spill over into April.
"We should be able to reschedule them and not have to delay other people; in other words, do the 30,000 at the same time as people we were planning on doing in the coming weeks as well."
He added: "What we've to do now is see what the EMA says. Our hope obviously is that they come back very positively.
"AstraZeneca itself has made the point that there have been less than 40 reports across Europe including the UK, that's 17 million people who have been vaccinated.
"AstraZeneca's statement goes further and says the incidence of blood clotting in the vaccinated population is actually less than you would see in the non-vaccinated population."
"So the hope is the EMA will come back very shortly with a positive result, and we'll crack on."
