Austria is likely to order a lockdown for unvaccinated people, its chancellor warns.

New lockdown restrictions for Austria’s unvaccinated population are likely because reports of new coronavirus cases in the country are rising rapidly, Chancellor Alexander Schallenberg said on Thursday.

Though such restrictions would be a “very harsh measure,” they appear to be necessary and “probably inevitable,” the chancellor said at a news conference on Thursday.

The Austrian national health agency has reported an average of 760 coronavirus cases a day for every 100,000 people over the past week, a rate that has more than doubled since late October.

About 64 percent of the country’s population has been fully vaccinated against the coronavirus so far — a larger share than in the United States or in Austria’s neighbors to the east, but smaller than in most Western European nations, according to government figures collated by the Our World in Data project.

The Austrian government said last week that it would ban people who are not fully vaccinated from entering places like restaurants and hair salons; that measure took effect on Monday. A lockdown like the one Mr. Schallenberg warned about would be much more restrictive.

“The situation in Austria and other European countries is serious,” Mr. Schallenberg said in a statement, noting that hospital intensive care units were filling up faster than expected.

The chancellor has been talking about the worsening picture in Austria for some time. “We are about to stumble into a pandemic of the unvaccinated,’’ he told The Associated Press last month.

At a news conference following a meeting with state governors last Friday, Mr. Schallenberg urged Austrians to get their shots.

“With a vaccination, we protect not only ourselves, but also our friends, family and colleagues,” he said, adding, “It is simply our responsibility to protect the people of our country.”