The warning comes as Germany is gripped by a third wave of coronavirus which is sweeping across much of Europe.
RKI president, Lothar Wieler, warned that if the spread is not curbed the country could be hit by as many as 100,000 new cases a day.
Mr Wieler told a press conference: “The current situation worries me very much. It is possible that we will see 10,000 new cases a day. It is possible that the virus will spread uncontrollably.”
He warned the current wave of coronavirus in Germany could be worse than the first two, as the country battles to contain the more infectious variant first detected in Kent.
Mr Wieler said: “We are at the beginning of a third wave. It was caused by variant B117.
“And this variant, as you all know, as we all know, is even more contagious and dangerous. And it is therefore also more difficult to curb this.
“There are very clear signs that this wave will be even worse than the first two waves.
“We have to prepare ourselves that the case numbers will increase significantly, that more people will get seriously sick again, that hospitals will be overwhelmed and that many people will also die.
“We are only at the beginning of this development and if we don’t immediately counteract this, then the consequences will be grave.”
Germany reported 21,573 new cases of the virus on Friday, taking the overall total since the start of the pandemic to 2,734,753.
The country’s death toll increased by 183 to 75,623, according to data from the RKI.
The warning comes after German Chancellor Angela Merkel made a U-turn on plans for a five-day shutdown over Easter.
Mrs Merkel on Tuesday announced an extension to Germany’s lockdown, along with a strict Easter shutdown in a bid to get a grip on spiralling Covid cases.
But on Wednesday she was forced to backtrack on her plans for tougher restrictions over Easter following a backlash, saying it was a “mistake” and that she took “ultimate responsibility”.
Mrs Merkel said: “This mistake is mine alone.
“The whole process has caused additional uncertainty, for which I ask all citizens to forgive me.
“There were good reasons for it but it could not be implemented well enough in this short time.”
Under the Easter plans, restrictions were set to be tightened between April 1-5 with Germans asked to stay at home and all shops closed.
It comes as much of Europe is facing a third wave of coronavirus.
Poland today reported a new daily record of 35,143 cases.
And Hungary’s prime minister Viktor Orban warned coronavirus restrictions cannot be eased due to rising infections.
Meanwhile, the European Union – which is facing intense criticism over its slow and chaotic vaccine rollout – is threatening to block exports of jabs.
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