Greece's international bailout has expired at midnight Tuesday, and with it any access the country could have to existing financing from its eurozone partners and the International Monetary Fund.
At the same time, the country defaulted on a roughly 1.6 billion euro IMF debt repayment, becoming the first developed country to fall into arrears on IMF payments.
Eurozone finance ministers had earlier declined to extend Greece's bailout on Tuesday just hours before its expiry and a possible IMF default, but talks will continue n Wednesday after Athens asked for a new aid plan, officials said.
"Last deadline for Greece program extension was weekend. Due to parliamentary procedures, unable to extend program beyond today," Slovakia's finance minister Peter Kazimir had wrote on Twitter following a conference call to discuss the last-minute proposal.
Finnish Finance Miniseter Alex Stubb said an extension was "not possible" and said a request for a new rescue programme with the European Stability Mechanism (ESM), the EU's bailout vehicle, "is always dealt with through normal procedures."
A Greek government source said the talks had concluded for the day and were set to resume Wednesday.
"The Eurogroup just finished. We will continue tomorrow morning to allow finance ministers to examine the proposals of the Greek government," the source said.
Prime Minister Alexis Tsipras had requested a two-year rescue deal with the European Union to save the crisis-hit country, just hours before its international bailout expires later Tuesday.
Tsipras also requested a short extension to its current bailout programme to avoid a "technical default," with a 1.5 billion euro payment due to the IMF in just hours.
The Eurogroup had previously rejected Greece's request for an extension to its bailout following the Greek government's announcement of a referendum on Sunday on reform demands by Athens' creditors.
The last country to do so was Zimbabwe in 2001.