French President Francois Hollande said today that countries including Spain and Greece had paid a heavy price to stay in the euro.
He also said it was "up to the Greeks" to decide whether to now remain a part of the single currency.
His comments in an interview with France radio came in reaction to a media report at the weekend which said the German government believed the euro zone would now be able to cope with Greece leaving the euro.
Germany's economy minister later said Germany wanted Greece to remain in the euro zone and there were no plans to the contrary.
"As for Greece remaining in the euro zone, Greece alone can decide," Hollande said.
"At this time we should not hypothesise about whether, according to the Greek vote, they would not or would still be a member of the euro zone. The Greeks are free to determine their own destiny," he added.
The question of Greece's continued membership in the euro zone has come into focus ahead of the January 25 parliamentary election that left-wing opposition party Syriza, which has promised to end austerity policies if elected, is seen winning.
Syriza leader Alexis Tsipras said in December his party would ask Europe to erase a big portion of its debt.
Hollande, whose Socialist government has criticised Germany's emphasis on budgetary discipline, said: "Europe cannot continue to be identified by austerity."
Meanwhile, a European Commission spokeswoman said today that a country's membership in the euro zone is "irrevocable".
She was responding to a question about Greece's possible exit from the single currency union following elections this month.