REUTERS - Greek Prime Minister Alexis Tsipras will summon an urgent meeting of his cabinet at 8 P.M. (5 P.M. GMT) on Sunday, state TV reported without giving further details.
Greece has said it may impose capital controls and keep its banks shut on Monday after creditors refused to extend the country's bailout.
A meeting of the country's Financial Stability Council was under way to discuss the situation in the country's banking system.
Greek President Prokopis Pavlopoulos met the head of the main opposition conservative party amid a political crisis and the threat of a debt default that would threaten Greece's future in the euro zone.
As head of state, Pavlopoulos normally plays a ceremonial role in Greek politics but he is responsible for appointing prime ministers and calling elections and will play a central role if the gathering crisis forces a change of government.
With Greece facing a chaotic period from Monday, when capital controls may be placed over its banking system, the leftist government of Prime Minister Alexis Tsipras has come under heavy pressure.
Its decision to call a referendum next Sunday on a foreign bailout has thrown open Greece's future as a member of the 19-member euro zone and could force Tsipras to resign if Greek voters defy its calls to reject the deal.
The government has urged Greeks to vote against the bailout terms, and Energy Minister Panagiotis Lafazanis on Saturday said there would be "political developments" when asked if the government would resign if Greeks voted 'yes'.
On Sunday, Pavlopoulos met former conservative Prime Minister Antonis Samaras, warning that it was vital for Greece to remain in the euro.
"The course of the country in Europe and in the euro zone must be undisturbed," he said, before the meeting. "I am confident that next Sunday, people will once more show that in crucial times it displays greater maturity and resolve."
As head of state, Pavlopoulos, a former conservative politician, normally stays clear of politics but was quoted by Greek newspaper Real News this month as saying that he would not be prepared to serve as president if the country left the euro.
However with Greece set to default on a 1.6 billion euro debt to the International Monetary Fund as early as Tuesday, even a "yes" vote in the referendum may not be enough to resolve the crisis and keep Greece in Europe.
Samaras, whose New Democracy party lost power to the leftist government of Prime Minister Alexis Tsipras in January, warned before meeting Pavlopoulos that Greece's position in Europe was under threat.
"We want to defend the position of Greece in the heart of Europe," he told reporters. "I am obliged to say that, right now, defending that national position is becoming harder, this 'red line' is in immediate danger".
He made no comments after the meeting with the president.
A U.S.-educated veteran of Greek politics, Samaras has condemned the decision by Tsipras to call a referendum on July 5 on bailout terms offered by foreign creditors and said during a parliamentary debate that it would force Greece out of the euro.
He has said in the past that he would be prepared to serve in a national unity government if Greece fell into crisis, as long as Tsipras were not part of it.
International Monetary Fund Managing Director Christine Lagarde said Sunday she is disappointed with the inconclusive outcome of talks with Greece, which is teetering on the brink of a default on its debt to the IMF.
At the same time, Lagarde said she is still willing to continue talks with the Greek government in the hope the country can make "appropriate structural and fiscal reforms" that are supported by "financing and debt sustainability measures."
"I continue to believe that a balanced approach is required to help restore economic stability and growth in Greece," she said.
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