Taoiseach Micheál Martin has said the Government's travel advice will be discussed by the Cabinet again this week.
Currently people are advised against travelling abroad, except in essential circumstances.
Speaking to the BBC, Mr Martin said: "We would be very cautious on international travel generally.
"And on the 20th July we will announce our measures in relation to international travel."
"Essentially the methodology will be in relation to the level of the disease in particular countries, including the UK, and in terms of the level and where Ireland will be.
"Countries that are at Ireland's level or below.
"And that’s the metric, if you like, that will determine our advice to Irish citizens in terms of their travel arrangements abroad.
"In terms of people coming into Ireland, the advice and the quarantining still remains, and it's under constant review.
"Why? Because there's a lot of international volatility with this virus.
"We’ve seen a spike in the numbers, we're very concerned about that and the Cabinet will be discussing this again this week in terms of measures that we may need to take to strengthen our resources at airports and so on to prevent the spread of this virus."
Meanwhile he said there needs to be 'an injection of momentum' on the Brexit talks.
"I think there has been some progress in terms of the paper that the UK government published.
"But we do need more detail, we need more precision.
"I think we need an injection of momentum into the overall talks between the European Union and the United Kingdom in relation to Brexit."
"I had a very fruitful discussion with the Prime Minister Boris Johnson after I took up office.
"I think we both agreed that it’s in everybody’s interest, particularly in terms of businesses and giving them certainty and securing employment into the future that we get a good, comprehensive trade deal between the UK and the European Union that can be tariff-free, quota-free, and that will facilitate smooth future relationships and good access to the single market in return for a level playing pitch all around."
On the prospect of a Brext deal, Mr Martin said: "I think there will be a deal. There has to be a deal.
"It can’t be at any price, and I think my obligation as Taoiseach of Ireland, and indeed all of our obligation as politicians, is to think of the people of Ireland, the people of the United Kingdom, the people of the European Union."
He added: "I see no sense in a no deal Brexit or in any sub-optimal agreement between the UK and the European Union.
"The ordinary people on the ground, the workers, will suffer if that is the case. "