Even though Athens' leftist government failed to come to an agreement with its international creditors overnight, a copy of draft proposals spoke of "extending" its bailout agreement as a "bridge" to a new package. Finance ministers in the Eurogroup will meet again on Monday to seek a compromise.
Meanwhile, the European Central Bank extended the amount of emergency liquidity assistance for Greek banks by 5 billion euros, on top of the 60 billion euros previously approved.
The extension drove up the shares of Greek banks, with the Athens Stock Exchange FTSE Banks Index rising 14.1 percent.
"It would appear that the Greeks are playing quite a good hand of poker," said Hantec Markets analyst Richard Perry.
The ECB's Governing Council earlier held a short-notice teleconference to discuss how long it could continue to keep Greek banks afloat.
Greek three-year yields were 270 basis points (bps) down at a day's low of 18.36 percent, while 10-year yields were down 60 bps at 10.36 percent <0#GRTSY=TWEB> in late session trading.
Athens' benchmark ATG equity index was up 6.7 percent, with National Bank of Greece's shares rising 18 percent. Piraeus Bank advanced by around 10 percent.
"We are continuing to take a glass-half-full view of these negotiations," Rabobank strategists wrote in a note, "although we do acknowledge that the path to resolution and dissolution remains worryingly the same."
Greek Prime Minister Alexis Tsipras will lay out his case for more financial help to fellow EU leaders in Brussels on Thursday.
(Additional reporting by Emelia Sithole-Matarise; Editing by Andrew Heavens)
By Sudip Kar-Gupta and John Geddie
