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Two German states with low coronavirus infection rates announced plans to throw off key public safety precautions, sparking anger and alarm Monday in Chancellor Angela Merkel's ruling coalition.

Thuringia and Saxony, both in the ex-communist east of the country, said they would "open up everything" with few exceptions from June 6, while monitoring for new outbreaks.

Under Germany's federalist system, the 16 regional states have far more leeway to set policy than in more centrally governed countries such as Britain and France.

Merkel has been widely praised for keeping the death rate in particular far lower than in many countries worldwide, even as she faced impatience from state premiers to accelerate the opening up of Europe's top economy.

But pressure has grown especially from regions less impacted by the virus to abandon national guidelines and give cities and towns the power to set the rules, while relying on "personal responsibility" for .

"I didn't say that people should start hugging each other or take off their masks to kiss each other," Thuringia premier Bodo Ramelow told public broadcaster MDR.

But he said it made "no sense" to maintain crisis measures when half of the districts in his state hadn't reported any new infections in the last three weeks.

Local health and safety offices should be given the power to monitor for outbreaks and react accordingly with the support of state authorities, he added.

Following Thuringia's lead, officials in Saxony said they were also ready for a "paradigm change" in the battle against the virus.

"Instead of imposing general rules and then allowing a lot of exceptions, essentially everything will be opened up and only a few exceptions will be made for what is not possible," regional health minister Petra Koepping said.

The announcements touched off angry reactions within Merkel's right-left "grand coalition".

Heath Minister Jens Spahn warned that such moves ran the risk of convincing Germans they could drop their guard.

"You must not create the impression that the pandemic is over," he told the Bild tabloid.

Lars Klingbeil, general secretary of the Social Democrats, junior partners in the coalition, accused Ramelow in particular of pandering to extremist critics of the safety measures who have staged loud protests in recent weeks.

"I expect politicians to lead and provide orientation and not be led by a few thousand people with standing up in public squares," he told Bild.

Bild reported Monday that the Merkel government intends to extend social distancing and mask wearing guidelines nationwide beyond the current deadline of June 5.