Travellers arriving in the Irish Republic from Britain will be asked to present a negative Covid-19 test.
The measure, which comes into force on Saturday, will also apply to people arriving from South Africa.
Anyone wishing to enter Ireland from those countries must be able to provide proof of a negative polymerase chain reaction (PCR) test taken within 72 hours prior to their arrival.
The ban on travel from Britain to Ireland, which had been due to end on Tuesday, has also been extended for 48 hours.
It comes after reports a more contagious UK variant of Covid-19 was found in about 25 per cent of cases in Ireland, up from the 10 per cent previously reported.
A separate variant, also believed to be more virulent, has also been discovered in South Africa.
International travellers will likewise be banned from boarding planes, trains and ferries to the UK unless they can present a negative PCR test taken no more than 72 hours before departure.
However, some government figures are thought to be pressing for British nationals and those resident in the UK to be exempt.
The Irish government is also considering a range of other Covid-19 restrictions to curb the pandemic.
A cabinet sub-committee on Tuesday put forward a number of new proposals, including closing schools, construction sites and creches.
Another measure to be considered is the closure of construction sites, apart from essential projects such as social housing or refurbishments.
Creches will also close but will still be available for children of essential workers.
Schools look set to close until the end of January at the earliest, as indicated by the Taoiseach on Tuesday.
It comes against a backdrop of rising coronavirus cases and admissions to hospitals and intensive care units.
Tuesday brought 17 further deaths linked to coronavirus and an additional 5,325 confirmed cases, the Department of Health said.
Additional reporting by PA