"The Russian banking system is stable, has sufficient capital reserves and liquidity to function without outages in any situation. All client funds are secure and available at any time," the central bank said in a statement.
Russia's domestic payment messaging system, developed in the event the country's banks are cut out of Swift, would continue to work "in any scenario," it added.
Late on Saturday, some people sat at the banks in front of empty ATMs waiting for fresh batches of cash to arrive. Many more went lining up in the early hours of Sunday, after the US and its European allies announced punitive measures on the Russian central bank and the country's biggest lenders.
"I withdrew money at the beginning of all this, and I am going to go search for an ATM again now. Because I want to have a month worth of cash in case there are technical glitches with cards. I already had problems paying for a taxi with Google pay yesterday," said Ekaterina, a Moscow resident.
"I believe my bank is not under sanctions, and I doubt my money will disappear altogether, but there is a risk I won't be able to buy food," she said. "We simply do not know what to expect of the government. I can't forecast, so I want cash to be around."
Bankers are worried of the effect such withdrawals will have on the banking system.
An executive at a western bank in Moscow said: "Their cash withdrawals are harming Russia, the banks' liquidity is falling."
Sanctions on the central bank limit its ability for forex interventions, which it had used before to stabilise the rouble and not let it into free float and collapse.
"I cannot even imagine the rouble tomorrow when trading opens up," the banker said on condition of anonymity. "The central bank will try to support [the rouble], the question is [for] how long. Non-residents are selling Russian assets, getting rid of the rouble and it is very bad for us."
Written by: Nastassia Astrasheuskaya and Max Seddon
© Financial Times