Cities across Germany braced for major protests against coronavirus restrictions on Monday, and a tough new vaccine requirement came into force in Italy as governments across Europe continued to tighten their rules in a struggle to contain the Omicron variant.

The developments in two nations where cases are rising fast — up 91 percent over the past two weeks in Germany, and more than 300 percent over the same period in Italy — encapsulate the tensions in European countries where leaders are doubling down on Covid vaccinations and boosters, beginning to make them all but mandatory.

More than 69 percent of people in the European Union have been fully vaccinated, according to official data, and the numbers are higher in the western part of the bloc, where Italy has vaccinated 75 percent and Germany 72 percent. With studies showing that the vaccines provide protection against severe illness and death from Omicron and other variants, governments increasingly see those who remain unvaccinated as an obstacle to avoiding more painful measures, such as reverting to lockdowns.

The challenge was expressed in harsh language last week by President Emmanuel Macron of France, who said in a newspaper interview that he wanted to “piss off” the millions of his compatriots who have declined the shots by barring them from public spaces. On Saturday, thousands of protesters took to the streets in opposition to a government proposal that would effectively ban unvaccinated people from public areas.

Vaccine skeptics also came out in big numbers in Vienna, where Covid shots will be mandatory for the entire adult population starting next month.

In Germany, where a strident anti-vaccination movement has ties to the far right, social restrictions and rules that shut the unvaccinated out of much of public life have prompted large protests on Mondays, a day that holds special resonance since weekly demonstration walks helped bring down the Berlin Wall in 1989. In recent weeks, tens of thousands of demonstrators have marched in cities and towns across the country, with some protests turning violent.

Last Monday, in the southwestern state of Baden-Württemberg, some 50,000 people took part in 170 marches. In the eastern state of Thuringia, the police in the town of Sömmerda used tear gas against a group of protesters. In Lichtenstein, a town in neighboring Saxony, 14 police officers were wounded in an attack by demonstrators, with one suffering a bite wound and another having to fend off an assailant who went for the officer’s weapon.

The recently elected chancellor, Olaf Scholz, has asked Germans to respect the restrictions and to get inoculated, and he used a New Year’s speech to rebut misinformation that the shots were unsafe. German lawmakers are expected soon to begin discussing legislation that would make vaccinations mandatory nationwide, but some members of Mr. Scholz’s coalition government are wary of the possible backlash.

In Italy, where opposition to vaccines is less fierce, a rule goes into effect on Monday that requires all public and private sector employees age 50 and older to be vaccinated against Covid or be able to show that they have recovered from the disease. Those who don’t meet the requirement by Feb. 1 could be suspended from work, part of the latest restrictions introduced by the government of one of Europe’s worst-affected nations to curb the steep rise of infections and mitigate the impact on hospitals.

With the Omicron variant fueling a doubling of the case rate over the past week, the Italian government has imposed the restriction on older workers because they are more susceptible to serious illness. Until now, those employees could take frequent P.C.R. tests that, if negative, allowed them to enter their workplaces.

Other new measures going into effect on Monday in Italy bar unvaccinated people from banks, offices, public transport, outdoor dining, hotels, ski lifts and a host of other places.