The move came after ministers held an emergency conference call.
Greek PM Alexis Tsipras had requested a short extension to Greece's current bailout, and a two-year rescue deal.
If it fails to repay the International Monetary Fund (IMF), Greece could risk leaving the euro.
Greece has also asked the IMF for more time, according to Deputy Prime Minister Yannis Dragasakis.
Eurogroup chairman and Dutch Finance Minister Jeroen Dijsselbloem said it would be "crazy" to extend the Greek bailout beyond its midnight expiration as Athens was refusing accept the European proposals on the table.
Speaking after the conference call, he added that a Greek request for a new €29.1bn European aid programme would be considered later.
The European Commission - one of Greece's "troika" of creditors along with the IMF and the eurozone's European Central Bank - wants Athens to raise taxes and cut welfare spending to meet its debt obligations.
Amid fears of a Greek default on its huge public debt of €323bn, people have queued at cash machines. Withdrawals are capped at just €60 a day.
Greek banks did not open this week after talks between Greece and its creditors broke down. However, up to 1,000 bank branches will re-open from Wednesday to allow pensioners - many of whom do not use bank cards - to withdraw up to €120
http://www.bbc.com/news/world-europe-33325886
