But Weidmann, who also sits on the European Central Bank's rate-setting Governing Council, said that he did expect a sustained recovery once the pandemic was fully overcome.
The pair's differing views reveals the rift over the main topic of debate on the ECB Governing Council as it prepares to decide next month on whether to extend the bank's 1.74 trillion euro asset-buying scheme.
Rajan was appointed to a three-year term, India's central bank said in a statement. He first joined the BIS board of directors in December 2013.
ECB policy-setters held the limit on their emergency funding for the banks steady for the second day running, a source familiar with their talks said, having previously increased it steadily over many weeks.
The Bank of Greece said the country's future in the European Union itself could also be at risk without a deal, underlining the extent to which officials who once refused any suggestion of "Grexit" are now openly discussing the prospect.
Greek Prime Minister Alexis Tsipras was under intense pressure to deliver crucial concessions to international creditors on Thursday to break a four-month deadlock and save his country from looming default that could pitch it out of the euro zone.
Jens Weidmann, head of the German Bundesbank and a decision-making member of the ECB's executive board today said that the Bundesbank had begun making asset purchases under the ECB's 1 trillion euro quantitative easing program. Speaking to CNBC's Carolin Roth, Weidmann said he sees little risks to the ECB's balance sheet from the QE programme.
The Cyprus bailout shows banks can be wound down despite difficulties, European Central Bank (ECB) policymaker Jens Weidmann said in an interview broadcast on Sunday, adding the situation on the island had stabilized.