However, German chancellor Angela Merkel said on arrival there was still no basis for re-opening talks with Athens.
“It is not a matter of weeks but of a few days” to save Greece from collapse,” Merkel said.
With Greek banks down to their last few days of cash and the ECB tightening the noose on their funding, Tsipras tried to convince the bloc’s other 18 leaders to authorise a new loan swiftly.
Merkel and French president François Hollande said after conferring on Monday in Paris the door was still open to a deal to save Greece from plunging into economic turmoil and ditching the euro.
Merkel, under pressure in Germany to cut Greece loose, made clear it was up to Tsipras to present convincing proposals after Athens spurned tax rises, spending cuts, and pension and labour reforms that were on the table before its €240bn bailout expired last week.
Eurozone finance ministers complained their new Greek colleague Euclid Tsakalotos, while more courteous than his abrasive predecessor, Yanis Varoufakis, had brought no new proposals to a preparatory meeting before the summit.
Greek officials said the leftist government broadly repeated a reform plan Tsipras sent to the eurozone last week before voters rejected the austerity terms previously on offer for a bailout.