All travellers arriving into Ireland from Britain and South Africa will have to provide a negative Covid-19 test.
From Saturday, there will be a new requirement for arrivals from those countries to have a negative PCR test within the preceding 72 hours.
This has been agreed by the Cabinet sub-committee on Covid-19 this evening and is subject to Cabinet approval tomorrow.
People will still be required to self-isolate for 14 days.
In the meantime, the travel ban from Britain and South Africa will be extended for 48 hours.
The restriction was due to expire at midnight tomorrow night, but will now remain in place until midnight on Friday night.
The Government will also move to bring in the same negative test requirement for other countries, but this is expected to take more time.
Dr Gerald Barry, a virologist at UCD, described the new requirement as "too late".
Speaking on RTÉ's Prime Time, he said the measure should have been brought in months ago.
Labour transport spokesperson Duncan Smith said the move does not go far enough.
He said: "This is far too late and smacks of the Government chasing its tail. Based on what has been reported it doesn't go far enough.
"What is needed is testing on arrival of passengers along with rigorous follow up to ensure people self isolate and don't develop Covid symptoms once in Ireland.
"Having testing in place at our airports and ferry terminals would give people a further level of confidence. It must now be delivered."