70% of the adult population should be fully vaccinated by the end of July, according to the Taoiseach.
30 to 39-year-olds are expected to be able to register for their jab next week.
Over 3.1 million vaccines have been administered so far - with registration still open for 40 to 69-year-olds.
Micheál Martin says Ireland is in a good position.
“I think we are in a good position,” he said. “I think the target we are aiming for is by the end of July – and this is a target-dependent on supply – that we will have 70% fully vaccinated.”
Mr Martin said the recent decision to shorten the interval between AstraZeneca doses would help the HSE hit the new target.
He said the 70% target is “in line with where Europe wants to be by the end of July.”
“June is going to be a very good month again,” he said. “The last two weeks of June are looking good in terms of security of Pfizer BioNTech in particular.