The justice and infrastructure ministers have called for an urgent meeting of the NI Executive.
On Saturday afternoon, the planned relaxation of Covid-19 rules in England, Scotland and Wales was cut from five days to just one.
In NI, no change has been announced to rules that allow three households to meet from the 23 to 27 December.
Naomi Long said urgent clarity was needed for families, while Nichola Mallon said “we need to act now”.
After the prime minister’s statement, the first and deputy first ministers spoke with the health minister, chief medical officer and chief scientific adviser.
Arlene Foster tweeted that it is “an evolving situation with the virus mutation”.
“Essential that we all play our part by following the regulations.”
Michelle O’Neill said discussions would continue over the weekend.
She said she had updated NI ministers and “more clarity is being sought” on travel arrangements.
“The executive will have to consider this urgently,” she tweeted.
A new six-week lockdown is coming into force at 00:01 GMT on 26 December, in a bid to suppress the spread of Covid-19.
When it was announced on Thursday, the executive said it would not affect the special Christmas rules allowing people from three households to come together for a period of five days.
Naomi Long said that with “Christmas just days away, [the] executive needs to meet tomorrow to provide clarity for families, particularly those planning to travel to form bubbles”.
“People need answers urgently,” she tweeted.
Nichola Mallon tweeted that “people are rightly concerned by reports tonight”.
“We need to act now and provide clear communication to the public,” she said.
A statement from the NI Executive was expected earlier on Saturday evening, but nothing has been issued.
It comes as Saturday’s figures show a further 17 Covid-linked deaths were recorded in NI and there were a further 640 cases of the virus, bringing the Department of Health’s death toll to 1,183.