Anyone who refuses an AstraZeneca vaccine will have to wait until the entire population is vaccinated to be offered an alternative, the Tánaiste has warned.
Leo Varadkar has said vaccinated people could be able to travel freely within the EU within months, but he has cautioned that travel in the future will be different.
Mr Varadkar has also confirmed that services, including hairdressers, will reopen next month and there will be a further lifting of restrictions on outdoor gatherings and activities from May 4.
"Over the course of the month of May there will be a phased reopening of personal services including hairdressers and barbers, but what we'll also do at the end of April, which not so far away now it's only two weeks away, we'll develop the plan for June and July," he said.
However, the Tánaiste warned that anyone who does not take up the offer of a vaccine will be put back to the end of the queue.
"They would have to wait until the end, and it's not possible to know when the end would be but it wouldn't be June or July, it would be later than that.
"The best option is the vaccine that's offered to you, and all the vaccines are effective and they're safe for the age groups they're indicated for."
Minister for Foreign Affairs Simon Coveney echoed the Tánaiste, saying anyone who decides not to take the AstraZeneca vaccine is “putting themselves to the back of the queue.”
Vaccines were safe, he told RTÉ radio’sshow, the benefits far outweighed the risks.
The more people who get vaccinated, the safer the country will be and the quicker restrictions would be eased, he added.
However, he acknowledged that there would be “bumps” along the way as issues arose and there would be a need to “recalibrate.”
The Government has to follow public health advice, he added. Irish people had responded very positively and people should trust the system, he urged.
Mr Coveney explained that decisions were being made by public health experts, not politicians.
The safest thing for people to do was to say yes to whichever vaccine was being offered, he said.
The minister warned if people were allowed to pick and choose, the vaccine rollout would not proceed at the pace needed.
Mr Varadkar said the promise to have offered a vaccine to 80% of adults before the end of June is "as a solid as it can be" and he said he is "confident" that this target will be met.
Turning to the issue of travel, the Tánaiste suggested that fully vaccinated people would soon be able to take a foreign trip.
"The European Union is developing a green cert, and we could see within months, people being able to travel again freely within the European Union, if they're fully vaccinated," he told RTÉ's Morning Ireland.
Mr Varadkar said some people will now circumvent mandatory quarantining by flying in via Belfast.
He added that problems around mandatory quarantine had been raised before its introduction and said there will be an "economic price" to pay if we "cut ourselves off for too long".
"Just because we made a decision to go down this route doesn't mean those problems went away. There are major legal, practical, political and humanitarian issues with this policy, and they are now playing out in court challenges and with capacity issues."
Striking a positive tone, Mr Varadkar said: "I know there has been a lot of news in the last couple of days about vaccines and quarantine and so on, but we shouldn't lose sight of the bigger picture, for the first time this year the number of people in hospitals is below 200, the number in ICU is below 50 cases, the R numbers is below one, kids are back to school the 5km rule is gone, we're building houses again."