According to a copy of the letter sent to Eurogroup President Jeroen Dijsselbloem and seen by Reuters, Varoufakis said Greece needed the extension beyond June 30 in order to take account of a referendum the government has called for next Sunday on whether to accept its creditors' latest offer.

"Our government will fully respect the outcome of the referendum and take this opportunity to reconfirm that Greece is an indivisible part of the euro zone," Varoufakis said. Prime Minister Alexis Tsipras has said voters should reject the offer.

"As the European Union's treaties make no provision for exiting EMU (European Monetary Union), the referendum ... does not raise directly or indirectly any issue regarding Greece's EMU membership," Varoufakis wrote.

(Reporting by Markus Wacket; Writing by Alastair Macdonald)