Germany is extending its lockdown until the end of January and banning non-essential travel in those areas worst-hit by the coronavirus pandemic, as it battles to control an upsurge in new infections.

“We are appealing to people to reduce their contacts to an absolute minimum,” Angela Merkel told reporters after a videoconference with the leaders of Germany’s 16 federal states.

The chancellor said infection rates were still too high and many hospitals were reaching the limits of their capacity. Germany also had to be “particularly careful” in view of the new viral variant spreading from the UK that was much more infectious than previous forms of the coronavirus, she said.

The leaders agreed to keep schools and kindergartens closed until the end of the month instead of relaxing restrictions from January 10. Shops and restaurants will stay shut too. They also imposed an unprecedented curb on movement, decreeing that in areas where the number of new virus cases is above 200 per 100,000 residents over seven days, travel will be limited to a 15km radius.

Ms Merkel said only those travelling for work or for a doctor’s appointment would be exempt from the new restriction, which is already in force in the two east German states of Saxony and Thuringia.

The leaders also toughened contact restrictions, decreeing that members of any one household will be allowed to meet only one other person in public. The current rule is that public gatherings are limited to five people from two households.

Germany has found it much harder to contain the latest wave of the pandemic than it did the first one last spring, despite a lockdown that has closed all schools, non-essential shops, restaurants, bars and theatres.

Authorities reported nearly 12,000 new infections with coronavirus over the past 24 hours, taking the total number of cases since the pandemic began to 1.79m. There were 944 Covid-19 deaths in the same time period. So far, 35,518 people have died of the disease in Germany.

“Whoever thinks they’ve conquered corona discovers that if they’re a little too quick [in easing restrictions], maybe too incautious, or too hopeful, the corona challenge catches up with them,” Markus Söder, Bavarian prime minister, said after Tuesday’s meeting.

He pointed out that the current statistics didn’t reflect travellers returning from their Christmas and New Year holidays, so the “number of unrecorded cases is probably quite high”. “For that reason we must assume the numbers will rise,” he said, adding that “lifting [the lockdown] too early would be the wrong thing to do”.

Tuesday’s decision came after the Germany government faced mounting pressure to speed up its Covid-19 vaccination campaign, amid claims from the opposition and some critical media that it ordered too few doses.

Some politicians have questioned why Germany delegated the procurement of vaccines to the EU, instead of ordering them on a unilateral basis.

Ms Merkel defended her government’s approach on Tuesday. “It was in Germany’s [national] interest that all 27 EU member states acted together to secure vaccines,” she said.

The chancellor said Germany was “surrounded by many EU member states, we are part of a free single market and we have the Schengen area where free movement is possible”.

“A high number of vaccinated people in Germany combined with a lot of people in neighbouring countries that aren’t vaccinated would not be to our benefit,” she said. “That’s why we do not want any national go-it-alone [approach].”