France and Germany urged Greek government to make credible proposals at a eurozone summit.
French president Francois Hollande said “The door is open for discussion,”.
Francois Hollande and German chancellor Angela Merkel had taken note of the message that sent by Greek political parties about their desire for staying in the eurozone.
He said “It’s up to Greek government to offer serious proposals so that this can be turned into a long-term perspective, because Greece needs a long-term program in the eurozone with stable standards.”
In the meantime, Greek banks have to remain closed on Tuesday and Wednesday. They were supposed to reopen on Tuesday, however, the Greek banking association leader said the period had been prolonged after the discussion on Monday.
The European Central Bank (ECB) said it would retain urgent funds aid for Greek banks as they are short of funds and nearly collapse.
However, banks have been advised to hold up more insurance with Greek banks as security against the €89bn (£63bn) of emergency lending.
This caused reduction of extra money that the banks have, and one of the main four Greek banks is already almost exhaust their funds.
The Economy Minister of Greece, Georgios Stathakis, said that the ECB had to maintain Greek banks survive for seven to 10 days so that negotiations could carry out.
Eurozone finance ministers intend to meet after a full summit of eurozone leaders on Tuesday.
Greek PM Alexis Tsipras has remarked that IMF appraisal confirmed that the reconstruction of Greek debt of more than €300bn (£213bn; $331bn) was essential.
However, German economy minister warned against any cancellation of Greek debt without restriction, saying that it would ruin currency unification.
German vice-chancellor, Sigmar Gabriel, said “I truly hope that the Greek government will accept that the other 18 member states of the euro can’t simply oblige an unconditional debt write-off.”
He also added “How could we refuse it to other member states? What would it mean for the eurozone if we’d do it? It would blow the eurozone separated without a doubt.”
Greek officials nominated Euclid Tsakalotos to take over Finance Minister Yanis Varoufakis, who resigned the post on Monday.
Mr Tsakalotos, aged 55 was born in Rotterdam and educated at Oxford, taught economics at Kent University in Britain between 1990 and 1993 before moving to Athens.
When he takes the office, he said that Greeks pronounced in a plebiscite that they “want better” and “inviable solution is not acceptable” to the debt crisis.
“We want to carry on the discussion. I believe something can change in Europe,” Tsakalotos said. He confessed to having “stage fright” upon assuming the post “not at the easiest moment in Greek history”.