Four people who tested positive for coronavirus in the last six weeks have been linked to American flights, according to the Minister for Health.
Stephen Donnelly told a press briefing this evening that nine out of 10 cases are domestic and that the measures address that.
Taoiseach Micheal Martin said the Government is "conscious" of the concern but "perspective is needed".
There has been widespread annoyance that flights from US hotspots are being allowed into Ireland, but the Government is happy people are following quarantine rules.
Taoiseach Micheal Martin addressed the nation this evening announcing the latest changes to restrictions, with Ireland now not moving ahead with phase four.
Micheal Martin said the aim is to get the R number back below 1 as the country battles against a rise in the spread of the virus.
It was earlier announced that the remainder of pubs will not reopen as planned next Monday following concerns about a rise in Covid-19 infections.
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Meanwhile, the wearing of face coverings will be made mandatory when shopping.
On Monday, the wearing of face coverings on public transport was made law, punishable by a €2,500 fine or up to six months imprisonment.
Retail staff will also be required to wear masks unless there is a partition between them and the customer or a distance of two meters.
After growing concern over the spread of the virus through house parties, the number of people allowed to visit an individual home has been reduced to 10, from no more than four different households.
In terms of holidays, the government is still advising against all non-essential travel.
A green list will be published on July 20 of countries with similar infection rates although people will still not be recommended to leave.
There will be increased staff at airports to monitor if passengers are quarantining upon arrival.
