Clashes broke out in the Netherlands on Sunday as anti-curfew demonstrators protested against coronavirus restrictions, while France imposed new border controls with several countries.
France introduced a requirement for incoming travellers from EU countries to show a recent negative coronavirus test.
It was a measure required for non-EU arrivals since mid-January and does not apply to those travelling by land, including thousands of cross-border workers.
In the US, Johns Hopkins University said the country had topped 25 million cases, remaining the hardest-hit after almost 99 million infections and more than 2.1 million deaths worldwide.
In the Netherlands, a Covid-19 testing centre was burnt in one village, while police used tear gas against demonstrators in Eindhoven, where cars were torched and businesses looted, and used water cannon and dogs in central Amsterdam.
"The fire in a screening centre in Urk goes beyond all limits," Health Minister Hugo de Jonge said.
The clashes came on the first day of a new curfew from 9pm to 4.30am, the country's first since the Second World War.
In Denmark, two men were arrested on Saturday night for burning an effigy of Prime Minister Mette Frederiksen at a protest against restrictions, while thousands marched against virus measures in the Spanish capital, Madrid.
Meanwhile Sweden said it would prohibit entry from neighbouring Norway for three weeks, after cases of the more transmissible strain that emerged in Britain were detected in Oslo.
In Egypt, a doctor and a nurse were the first on Sunday to receive the vaccine from the Chinese company Sinopharm.
"All healthcare workers will receive it for free, it's their right," Health Minister Hala Zayed said.
Ms Zayed said more than 300 doctors had died of Covid-19 in Egypt.
She said Cairo had signed deals to receive vaccine shipments from British, Chinese and Russian companies, for 100 million doses, enough for about half of Egypt's population.
Israeli Prime Minister Benjamin Netanyahu said the country was "closing the skies hermetically, except for rare exceptions" to incoming and outgoing traffic for a week.
Israel is in its third national coronavirus lockdown, initiated in late December and extended on Tuesday until the end of the month because of a surge in Covid-19 deaths.
Israel is well advanced in its vaccination drive, with more than 2.5 million of its nine million people vaccinated in a month.
The US passed 25 million cases days after it recorded 400,000 deaths.
President Joe Biden this week warned that the toll could rise to 600,000 fatalities, but he hopes to distribute 100 million vaccine doses within his first 100 days in office.
Vivek Murthy, Mr Biden's nominee for surgeon general, told ABC on Sunday that the target was "a floor, not a ceiling", and said new strains were "very concerning".
Large countries such as Brazil and India have faced vaccine struggles, as organisational failings and public fears over side effects hamper progress.
Experts have warned that Brazil could run out of vaccine doses and crucial equipment such as syringes.
They say its vaccine sceptic President, Jair Bolsonaro, could be endangering supplies with criticism of Sinopharm's CoronaVac shot.
In India, about a third of people are not turning up for vaccine appointments, with fear of side effects after reports of a few cases of severe reactions spread widely through the media and messaging services.
"I am very afraid. I hate needles and I am worried about side effects," said pharma student Khushi Dhingra, 17, with tears in her eyes as she waited in line for the vaccine at Sharda Hospital in Greater Noida, near New Delhi.
European health authorities say there is no evidence that the vaccines were to blame in the deaths of a small number of nursing home residents.
Germany said Sunday it had paid €400 million ($487m) for 200,000 doses of the experimental antibody treatment used on former US President Donald Trump.
In New Zealand, officials confirmed the first case of Covid-19 in the community for more than two months.
It was found in a woman, 56, who had recently returned from Europe.
And in Britain, Sky TV said Kenneth Branagh would star as Prime Minister Boris Johnson in a TV drama about the country's handling of the outbreak.
Director Michael Winterbottom said the show, set to air on Sky Atlantic next year, would focus on "the efforts of scientists, doctors, care home workers and policy makers to protect us from the virus".