Northern Ireland's Deputy First Minister has said travellers arriving from other parts of the UK should have to self-isolate for 14 days.
Michelle O'Neill said the move is needed because the greatest risk of a resurgence of the virus north of the border is posed by people arriving from Britain.
Sinn Féin's leader in Northern Ireland said "the issue of travel from Britain is a very real threat that we have to face up to".
She said she will propose introducing a quarantine requirement from visitors from Britain when the Stormont Executive meets to discuss the issue on Thursday.
First Minister and DUP leader Arlene Foster has made it clear she opposes such a move.
Speaking in Ballymena earlier, Mrs Foster said it was not for her to tell people whether they should proceed with foreign holidays.
She noted there were around 60 countries on Northern Ireland's green list and people travelling to and from those destinations would not have to self-isolate when they come home.
"It's not up to me to tell people should they go or should they not go," Ms Foster said.
"If they have booked a holiday and they (the destination) are on the green or amber list then they can go without having to quarantine when they come back.
"Whether they go or not is entirely a matter for their own judgement."
Ms Foster said Stormont officials were looking to "tidy up" the coronavirus regulations to keep them in line with recent decisions taken by the executive.
Speaking in Co Tyrone this afternoon, Ms O'Neill reiterated her party's view that there should be an all-island approach to combating Covid-19.
"My biggest concern in terms of travel from Britain would be the fact that the community transmission there is so much higher, and probably the biggest risk that's posed to us here right now is the travel from Britain," she said.
"When we look at where is the greatest risk posed, the greatest risk that we have been told is from travellers coming from Britain.
"So the Executive has to take, has to have a discussion about that issue, and actually make a call on it but certainly, it's my view that, given that that's where the greatest risk comes, then we need to we need to act on that."
For the seventh consecutive day, no further coronavirus deaths were recorded in Northern Ireland, so the official death toll remains at 556.
There were 23 new cases, taking the total number of cases to 5,857.
The Deputy First Minister said the travel arrangements will be on the agenda when the North-South ministerial council meets next Friday for the first time in more than three years.
She also stressed that the decision by the Stormont Executive earlier this month to exempt more than 50 countries from quarantine arrangements was aimed at travellers making essential journeys and not to facilitate holidays.
"People are naturally asking the question about travel, should they travel and can they travel, certainly my constituency office is inundated with people asking that question," she said.
"So I want to be very cleat to people, to give them a very strong message again from the Executive currently remains that there should be no non-essential travel, people are advised not to travel at this time."
Ms O'Neill said the Alliance Party's health spokesperson, Paula Bradshaw MLA, was right to cancel a planned family holiday to Italy.
The MLA for South Belfast had initially insisted she would not be breaching Covid-19 restrictions by travelling, but later said she had decided to cancel the trip.
The Deputy First Minister also said it was important that the message and approach to the virus across the island of Ireland is the same.
"When we look back over the last four months, we've been most effective when we've worked as an island unit in terms of containing the virus," she said.