Chancellor Angela Merkel on Sunday urged Germany's 16 federal states to honour measures agreed to curb Covid-19, with cases spiralling as many regions stray from the national line.

"We need action in the federal states," Merkel said in an interview with the ARD broadcaster.

"We have to take the appropriate measures very seriously. Some states are doing it, others are not yet doing it," she said.

At a tense meeting last week, Merkel and the regional leaders had agreed to stick to shutdown measures including an "emergency brake" to be applied in regions with high incidence rates until April 18.

But under Germany's federal system, each state can ultimately decide its own rules and some have continued with reopening steps, despite fierce criticism.

The small southwestern state of Saarland has said it is planning to end its shutdown completely and open leisure, sports and entertainment facilities after Easter to those who can provide a negative test.

"If we are creating the impression that we can still open things -- that is not the order of the day at the moment," she said.

Germany was widely praised for its handling of the first wave of the pandemic, but has struggled to contain new infections since they began spiralling out of control in a second wave late last year.

Cases had started to come down after Christmas but the British variant has led to a dramatic spike in recent weeks, just as the country was taking first steps towards reopening.

Merkel and the regional leaders had also last week agreed to a short, sharp shutdown over Easter, with almost all shops to be closed and citizens urged to stay at home.

But they reversed that decision two days later, acknowledging that there were prohibitive hurdles to shutting the economy down for five days with so little notice.

Facing calls for a confidence vote in parliament, Merkel took the blame for the climbdown in a rare public apology, asking Germans to forgive her for the "mistake".

Germany's Robert Koch Institute (RKI) health agency reported 17,176 new cases in 24 hours on Sunday -- almost 3,500 more than last Sunday -- and an incidence rate of 129.7 cases per 100,000 people over seven days.