But the institute said the delay in reporting data from the large state of Saxony could be part of the reason for the spike.
Data was not sent out from Saxony on Monday, so Wednesday’s report includes the missing numbers for Monday as well as Tuesday.
The record daily increase in the number of cases registered on December 11 was 29,875.
German leaders have sounded the alarm in recent days as the country faces a frightening spike in coronavirus cases, hospitalizations and deaths.
The head of RKI said on Tuesday that the situation is “as grave as it has been during this epidemic”.
Lothar Wheeler said: “At the moment, a very large number of people are infected,” adding that Germany needs to prepare for “the exacerbation of the situation during Christmas.”
German Health Minister Jens Spahn joined a number of other European countries in calling for the European Medicines Agency (EMA) to approve the vaccine soon.
He said Germany would be ready to start vaccinating the population after “two to four days” after approval.
“The aim is to get the approval before Christmas. We want to start vaccination in Germany before the end of the year,” Spahn told reporters at a news conference.
President Frank-Walter Steinmeier addressed the nation on Monday in a rare speech, describing the situation as “extremely dangerous”.
“From Wednesday onwards, our public and private life will be more restricted than what we have seen in the history of the Federal Republic of Germany,” he said, adding that “strict measures cannot be avoided.”
Merkel warned the German parliament a week ago that the nationwide restrictions imposed on November 2 were ineffective and that measures were needed to prevent the explosive growth in numbers.
“If we had a lot of contacts now before Christmas, and ended up making it the last birthday with grandparents, then we would have failed. We shouldn’t do that,” she said in an unusually enthusiastic speech.
The head of RKI’s monitoring unit, Ute Rexroth, has released increasing numbers of infections and potential deaths, and said Germany is seeing twice the number of infections in care homes compared to the first spike in the coronavirus this spring.
The startling new numbers are a major concern, and could send the world’s fourth largest economy into another recession. It is a stark warning to other countries grappling with the winter tide of Covid-19.
An earlier version of this story misrepresented the gap in the Saxony numbers released on Wednesday. Included Monday as well as Tuesdays.
CNN’s Emma Reynolds and Nadine Schmidt contributed to this report.