A banking official said the tentative plan was to keep Greek banks closed at least a week.

There is still a chance that Greece and its creditors — the European Central Bank, the International Monetary Fund and the other eurozone countries — can come to terms before its current bailout program expires on Tuesday. On Sunday, the European Commission and I.M.F. issued statements indicating the door to further discussions might still be ajar.

And in Washington, the White House issued a statement saying that President Obama and the Chancellor Angela Merkel of Germany had spoken by phone Sunday. “The two leaders agreed that it was critically important to make every effort to return to a path that will allow Greece to resume reforms and growth within the eurozone,’’ the White House statement said.

But the European Central Bank, for its part, declined on Sunday to raise the limit on its emergency funding for Greek banks — a level currently said by banking officials and analysts to be around 89 billion euros, or about $100 billion — even though businesses and consumers have withdrawn billions of euros in recent weeks.

That rate of withdrawals appeared to increase over the weekend, as long lines formed at A.T.M.s around the country, threatening a bank run that the Greek government could try to avoid by imposing capital controls. But at the same time, the European Central Bank did not cut off support entirely, giving the Greek government some extra flexibility in the coming days.

Greece’s own central banker, Yannis Stournaras, said in a statement after the European Central Bank decision on Sunday that the Greek central bank would “take all measures necessary to ensure financial stability for Greek citizens in these difficult circumstances.”

Before negotiations broke off on Saturday between Athens and its creditors, the Tsipras government had been hoping to reach terms that would free up a €7.2 billion allotment of bailout money that the country needs to meet its short-term debt obligations.