Official figures showed more than 30,000 newly confirmed cases in Germany over the past 24 hours, an increase of about 50 per cent compared to a week ago.
Hospitals have warned that ICU capacities are nearly exhausted, with some patients having to be transferred to clinics some distance away.
Health minister Jens Spahn urged Germans to get vaccinated, including with booster shots if their first round of inoculation occurred more than six months ago, to reduce the risk of serious illness.
"By the end of this winter pretty much everyone in Germany ... will have been vaccinated, recovered or died," Mr Spahn told reporters in Berlin.
He acknowledged that some had described this view as cynical.
"But it's true," he said. "With the highly contagious Delta variant this is very, very likely and that's why we are recommending vaccination so urgently."
Mr Spahn said some 50 million doses of the Moderna and BioNtech/Pfizer vaccines would be made available for the rest of the year to allow people to get first, second or third jabs, as necessary.
To achieve this, Germany was holding back tens of millions of doses originally intended for poor countries. These missing doses would be provided at a later date, he said.
Some politicians in Germany have suggested the country may need to consider compulsory vaccinations, like its neighbour Austria.
About 68 per cent of Germany's population of 83 million has been fully vaccinated. The German government has said it wants to push that rate above 75 per cent to effectively curb the spread of the virus, but a sizeable minority in the population has resisted calls to take the vaccine.
Karl Lauterbach, a prominent politician with the the centre-left Social Democrats, called for a "radical" application of rules requiring people to present vaccination or recovery certificates to access some shops and public places.
"A general vaccine mandate (shouldn't be) taboo either," he said on Twitter.
Bavaria's conservative governor, Markus Soeder, said on Monday that he also favoured mandatory vaccines for all.
Mr Soeder acknowledged that such a move would infringe on civil liberties, but argued that this needed to be balanced against the need to protect the health of the population and preserve other freedoms.
"That's why we believe that only a general vaccine mandate offers a durable solution," he added.
But a spokesman for outgoing German chancellor Angela Merkel made clear that her government had no plans to tackle the controversial issue of vaccine mandates.
"There is no decision about this now and it wouldn't be taken by this government anymore," Steffen Seibert told reporters in Berlin.
A centre-left coalition of three parties is expected to finalise negotiations on forming a government in early December.
Germany expects the European Union to approve vaccines against COVID-19 for children aged five to 11 at the end of the week, he said.
School-age children have among the highest infection rates in the country.
The EU will begin shipping vaccines adjusted for younger children on December 20, with Germany initially getting 2.4 million doses, Mr Spahn said.
