France will do all it can to keep Greece in the eurozone, because allowing it to leave would be too risky, Prime Minister Manuel Valls has said, reports BBC News.
"The basis for a deal exists," he said ahead of an emergency eurozone summit.
However, Germany has warned against any unconditional debt write-off.
Eurozone ministers have called on Greece to put forward fresh proposals after Greek voters rejected the latest draft bailout deal in a referendum.
Greek Prime Minister Alexis Tsipras met Greek political party leaders on Monday and headed to Brussels on Tuesday morning, where he is expected to present new proposals.
His plan is said to include a demand for Greece's vast 323 billion euros ($356bn; £228bn) debt to be cut by up to 30%.
Greece's teetering banks are to stay closed on Tuesday and Wednesday.
The European Central Bank (ECB) is maintaining its pressure on the banks, refusing to increase emergency lending and ordering them to provide more security for existing emergency loans.
Mr Tsipras met Greek political party leaders on Monday to agree a collective negotiating stance. According to Greek media, the demands include: securing liquidity for Greece's financial system; credible reforms with reduced recessionary impact; strong programme for growth; restructuring of Greek debt - that could mean writing some off and rescheduling repayments.
After their meeting, Greek political leaders released a joint statement insisting that the country should remain in the eurozone.
"The recent verdict of the Greek people is not a mandate for rupture, but a mandate to continue and strengthen the effort to reach a socially fair and economically viable deal," the statement said.
In his comments on Tuesday, Mr Valls said the eurozone could not "take the risk of Greece leaving" - for economic as well as political reasons.
"There is no taboo subject when it comes to [Greek] debt," he told French radio.
France and Germany have urged Greece to come up with "precise" fresh proposals - but differ over how much they should compromise to find a deal.
Germany is taking a tougher line than France, say correspondents - warning against any unconditional write-off of Greece's debt, amid fears it would destroy the single currency.