The Tánaiste says it will likely be later summer or early autumn before people are able to fly abroad.
However, Leo Varadkar says it would be "common sense" to allow people travel to and from England, Scotland and Wales as a "first step" in resuming international travel.
Mr Varadkar was speaking on what he described as a "day of hope and a day of freedom" for Ireland, amid a major easing of COVID-19 restrictions.
Inter-county travel is allowed from today, while thousands of businesses and cultural attractions are allowed to reopen for the first time this year.
Around 12,000 businesses are expected to reopen over the course of the week, with 100,000 people returning to work.
Speaking on Newstalk Breakfast, Mr Varadkar said this is a much slower reopening than we had before Christmas - but plans are on track for the coming months.
He said: "People are right to be cautious and maybe a little bit worried.
“It’s still the case that two-thirds of adults haven’t had the vaccine yet - we need to go a little bit slowly.
“If things work out… I think we can be confident we’ll have outdoor hospitality in June as planned… and from July we’ll be able to go indoor dining."
He said he expects the summer months to be "very similar" to last year - not fully back to normal, but with "pretty much all businesses open".
In terms of foreign travel, Mr Varadkar said: “Certainly we will be opting into the EU green cert [system], but it may be later in the summer or early autumn [before] that actually means something in terms of being able to fly.
"Even then, you just don’t know whether there’ll be an outbreak in the country you want to fly to."
However, he said he'd like to see proper consideration to the full restoration of the Common Travel Area between Britain and Ireland.
He noted that the UK is ahead of Ireland in terms of the vaccine programme, while the incidence of the virus is lower there.
He said it's "common sense" to allow people travel to England, Scotland and Wales - and vice versa.
The Tánaiste also said some form of mandatory hotel quarantine is likely to remain in place for the foreseeable future.
He said: “I could see the removal of mandatory hotel quarantine for travel to vaccinated places… but I could see it remain an option for quite some time for places where the virus is still raging.”
