Last week authorities extended some COVID lockdown curbs until Jan. 18, including the temporary closure of hospitality venues and non-essential retailers.
Health emergency coordinator Fernando Simon blamed the surge on lax restrictions over the Christmas holidays and said he expected the increase to continue for some time.
The pan-European STOXX 600 index advanced 0.5pc to near February 2020 highs, while London's blue-chip FTSE 100 gained 0.2pc and Germany's DAX index was up 0.6pc.
Schools will not reopen until January 11 in order to delay for as long as possible the return to classrooms after the family gatherings over Christmas.
Japan declared a limited state of emergency in the capital, Tokyo, and three neighbouring prefectures on Thursday to stem the spread of the coronavirus.
Prime Minister Yoshihide Suga’s government is seeking to limit damage to the world’s third-biggest economy while striving to defeat the virus once and for all as it looks ahead to staging the postponed summer Olympics.
Britain began its third COVID-19 lockdown on Tuesday with the government calling for one last major national effort to defeat the spread of a virus that has infected an estimated one in 50 citizens before mass vaccinations turn the tide.
Britain has been among the countries worst-hit by COVID-19, with the second highest death toll in Europe and an economy that suffered the sharpest contraction of any in the Group of Seven during the first wave of infections last spring.
"We need to restrict contact more strictly... We ask all citizens to restrict contact to the absolute minimum," she told journalists following a meeting with the leaders of Germany's 16 federal states.
Even if a first test was negative, travellers from risk regions would in future have to enter quarantine for five days and take a second test, Merkel said.
Johnson said more than 1.3 million people had been vaccinated as of Tuesday afternoon, adding that nearly 1,000 vaccination sites would be ready by the end of the week.