Eurozone finance ministers say they expect to hear new proposals from Greece after the country voted to reject the terms of a bailout.
German Chancellor Angela Merkel and her French counterpart Francois Hollande also called on Greece to make "serious" proposals.
Greek PM Alexis Tsipras is due to address a summit of eurozone leaders on Tuesday.
Meanwhile, Greek banks are to stay closed on Tuesday and Wednesday.
They had been due to reopen on Tuesday but the head of the Greek banking association, Louka Katseli, said the period had been extended following talks on Monday.
In another development, the European Central Bank (ECB) said it would maintain emergency cash support for Greek banks, which are running out of funds and on the verge of collapse.
However, BBC economics editor Robert Peston says banks have been told to lodge more collateral with the Bank of Greece as security against the €89bn (£63bn) of emergency lending.
This reduces the amount of spare cash that the banks have, he adds, and one of the big four Greek banks is understood to have already almost run out of cash.
Greece's Economy Minister, Georgios Stathakis, had earlier told the BBC that the ECB had to keep Greek banks alive for seven to 10 days so that negotiations could take place.
(BBC)