German virus deaths top 40,000
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More than 1.9 million people have been infected so far, with almost 17,000 new cases added since Saturday.
In her weekly video message on Saturday, Merkel said the full impact of socialising over the Christmas and New Year's period was yet to show up in the statistics.
She warned Germans that "these next winter weeks will be the hardest phase of the pandemic" so far, with many doctors and medical staff working at their limits.
Germany fared better than many other European countries during the first Covid-19 wave in the spring but it has been hit hard by the second wave.
The nation of 83 million people, the bloc's most populous, has imposed another round of restrictions to limit social contacts and help hospitals cope with a surge in patients.
More than 5,000 Covid-19 patients are currently in intensive care nationwide, with over 80 percent of intensive care beds occupied.
Germany has closed schools and non-essential shops, culture and leisure facilities until at least January 31 in hope of slowing the outbreak.
Like other EU nations, it started vaccinating citizens against Covid-19 in late December using the Pfizer/BioNTech jab.
More than half a million people have received the jab so far.
A second vaccine, developed by US firm Moderna, will join the rollout in the coming days.
- 'Absolutely necessary' -
Merkel acknowledged the vaccine campaign had got off to a slow start, "but the tempo will pick up", she said.
"What's important is that we can say: we will have enough of the vaccine available for everyone in Germany," she added.
"Month after month we will inoculate more people and eventually we will be able to offer the vaccine to anyone who wants it."
Merkel said the vaccines allowed for "justified hope" that the world could conquer the pandemic.
But she urged Germans to stay patient and said she was "firmly convinced" the current tough curbs on public life are "absolutely necessary".
A survey by the Kantar research group for Bild am Sonntag newspaper found that 56 percent of Germans agreed with the latest measures to stem the virus spread.
Another 25 percent of respondents said the restrictions did not go far enough.
Just 16 percent said the rules were too strict.
The number of fatalities in Belgium from the new coronavirus crossed 20,000 on Sunday, health officials said, with more than half the dead from retirement care homes.
The country, with a population of 11.5 million, has recorded 662,694 cases and 20,038 deaths since the pandemic broke out, the Sciensano public health institute said.
Belgium counts all deaths of people who have had a positive Covid-19 test among virus fatalities, giving it one of the world's highest death rates with 1,725 per 100,000 people, according to an AFP tally.
Covid-19 vaccinations began in Belgium on January 5.
During the first wave of the pandemic Sciensano reported more than 250 deaths a day with a peak of 322 on April 8.
The figures improved during summer but began rising again in October with 218 daily deaths recorded on November 10. The average number of deaths reported last week was 58 a day with about 1,780 infections.
More than 1.9 million people worldwide have now died from the virus, with new variants adding to soaring cases and prompting the re-introduction of restrictions on movement across the globe.