0352 GMT January 21, 2021
In Sweden, people have been told to prepare for possible travel restrictions during the holiday period, BBC News reported.
Meanwhile Irish and French authorities said it was too soon to say if people could make travel arrangements.
With six weeks until the festive season, lockdowns and other measures are in force in several countries.
Portugal has significantly expanded the number of places subject to a night curfew. From Monday, three-quarters of the country will be under the government's toughest restrictions.
Sweden's top state epidemiologist Anders Tegnell told citizens to prepare for the possibility of restricted travel between different areas during the Christmas period so that regional health care services could avoid becoming overwhelmed.
A provisional decision would likely be made in a week or two, he said, adding that Swedes needed to be prepared that things could still change "right before Christmas."
Meanwhile, Irish Deputy Prime Minister Leo Varadkar said he would not yet advise Irish citizens living abroad to book flights home, adding that it was "too soon" to give such advice.
A similar sentiment was shared by French Prime Minister Jean Castex, who said it was "too early" to say whether citizens could buy train tickets to travel at Christmas.
He added that there would be no easing of lockdown restrictions for at least two weeks. "It would be irresponsible to soften the lockdown now," he told a news conference, "the gains are fragile."
Under the lockdown restrictions, people in France can only leave their homes to go to work if they cannot work from home, to buy essential goods, seek medical help or to exercise for one hour a day. All nonessential shops, restaurants and bars are shut, but schools and crèches remain open.
Castex added that some shops may be allowed to reopen from December 1, depending on case numbers. But he said bars and restaurants must remain closed.
France is grappling with a sharp rise in cases, with more than 1.9 million confirmed infections, according to a tally by Johns Hopkins University.
On Thursday, French health authorities announced a record-high 32,638 hospitalizations — almost 350 higher than a peak reached in April.
In Italy, much of the country is in lockdown, but there are calls for stricter measures as the numbers of infections continues to grow. A further 636 deaths were reported on Thursday. Regional Affairs Minister Francesco Boccia said people should celebrate Christmas only with close family members.
In the UK, discussions took place about the four nations taking a joint approach to COVID rules over Christmas.