The ECB Governing Board board said it "decided to maintain the ceiling to the provision of emergency liquidity assistance (ELA) to Greek banks at the level decided on Friday".
"The Governing Council stands ready to reconsider its decision," it added in a statement.
The Frankfurt-based bank has been the lifeline keeping Greek banks -- and by extension the Greek state -- afloat with the ELA emergency cash through five months of tortuous negotiations that have now taken a sharp turn for the worse.
As fears grew of financial markets turmoil and contagion on Monday, it also said "the Governing Council is closely monitoring the situation in financial markets and the potential implications for the monetary policy stance".
The ECB -- which has maintained ultra-low interest rates and launched large-scale quantitative easing measures -- said it "is determined to use all the instruments available within its mandate" to maintain price stability.
Bank of Greece chief Yannis Stournaras said in the same statement that his bank "will take all measures necessary to ensure financial stability for Greek citizens in these difficult circumstances".
ECB head Mario Draghi said "we continue to work closely with the Bank of Greece and we strongly endorse the commitment of Member States in pledging to take action to address the fragilities of euro-area economies."
The announcement suggests that a short-term compromise has been reached between Greece and its creditors. However, the ECB did not vote to increase emergency funding — currently said by analysts to be around 85 billion euros — even though businesses and consumers have reportedly withdrawn more than a billion euros in recent days.
This weekend there have been long lines at ATMs throughout Greece, following the collapse of talks on Saturday to reach agreement on austerity measures put forward by Greece's creditors. The Greek prime minister's decision to refer the measures to the Greek electorate in a referendum next Sunday precipitated the failure of the talks.
Greek officials were meeting Sunday afternoon, in what analysts expected to be discussion of whether to impose capital controls — strict limits on how much money businesses and consumers can withdraw. Declaring a bank holiday — keeping the banks closed on Monday — is also a possibility.
France's prime minister, Manuel Valls, earlier urged Greece and other nations to do whatever they can to keep Greece in the 19-nation bloc that uses the euro currency.
Valls said on Sunday that "we don't know — none of us — the consequences of an exit from the eurozone, either on the political or economic front. We must do everything so that Greece stays in the eurozone." He was speaking on France's i-Tele TV.
Valls added that "means respecting Greece and democracy, but it's also about respecting European rules. So Greece needs to come back to the negotiating table.”
Meanwhile, the German foreign ministry recommended Sunday that Germans travelling to Greece to "take sufficient amounts of cash” as the country was hurtling towards a banking crisis.
With Greece a top vacation spot for Germans, the foreign ministry urged tourists them to keep tabs on the evolving situation and check for any updates to its travel recommendations.