The radical leftist Greek government is on the verge of default and needs an agreement to unlock 7.2 billion euros (USD 8.1 billion) in bailout cash before its international rescue package expires at the end of the month.
Athens and Brussels traded barbs over the weekend after Tsipras rejected a plan put forward by European Commission chief Jean-Claude Juncker last week, but today Greece relented and sent in its counter-offer.
Tsipras has requested a meeting with German Chancellor Angela Merkel and French President Francois Hollande on the sidelines of an EU-Latin American summit tomorrow to discuss the crisis.
Schinas would not indicate whether Juncker would take part in the meeting, saying Brussels had to study the new Greek plan first.
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Last week the Greek premier testily rejected Juncker's "absurd" plan following a meeting with the EU executive chief,
In an emotional interview published today, Tsipras said any failure to reach a deal would be a catastrophe for the 19-nation euro area.
"I think that is evident. It would be the beginning of the end for the eurozone," Tsipras told the Italian newspaper Corriere della Sera.
Greece's five-year debt crisis surged back as an international concern in January after Tsipras's radical Syriza party won elections on a vow to end painful austerity measures made as part of the country's 240-billion-euro bailout since 2010.
The Syriza-led government has since been locked in a four-month standoff with its dissatisfied creditors. Greece has offered reforms on pensions, VAT and the country's primary surplus, but has also demanded debt relief and insisted on its own social programmes.