German chancellor Angela Merkel has said both she and new French President Francois Hollande want Greece to remain in the eurozone.
She said they were ready to help the crisis-stricken country to return to economic growth.
Speaking at a joint news conference with Mr Hollande, the chancellor also said that Germany and France understand their joint responsibility for Europe and must offer joint ideas at an EU summit next month on reviving economic growth.
Mr Hollande said Europe should consider all possible measures that could spur economic activity and growth.
The meeting between the two leaders was delayed this evening after Mr Hollande's presidential jet was struck by lightning shortly after take-off.
The new president took off a short time later in a different plane.
Mr Hollande was sworn in as France's first Socialist president in 17 years this morning.
Outgoing president Nicolas Sarkozy greeted Mr Hollande at the Elysee Palace and transferred the nuclear codes and other secret files.
Mr Hollande said he wanted to "open a new path" in Europe in a speech after his inauguration.
"Such is the mandate I have received from the French people on May 6.
"Put France back on its feet with justice, open a new path in Europe, contribute to world peace and to the preservation of the planet.
"I am addressing a message of confidence to the French people. We are a great country that has always risen to its challenges," he said, also vowing that he would run the country with "dignity and simplicity".
"I take stock today of the force of the pressures our country is under: massive debt, feeble growth, high unemployment, damaged competitiveness, a Europe that is struggling to get out of the crisis.
"Nothing is inevitable as long as we are driven by a common will, as long as a clear course has been set, and we apply all our strength and the assets of France."
Anxious not to lose the "Mr Normal" image that appealed to voters tired of his showman predecessor, Mr Hollande asked for his inauguration ceremony to be kept as low-key as possible.
In a break with tradition, he invited just three dozen or so personal guests to join some 350 officials at the event and neither his nor his partner Valerie Trierweiler's children attended.
He was then taken on a traditional victory spin down the Champs Elysees in an open-topped car.
Mr Hollande is set to name civil servant Pierre-Rene Lemas as his chief of staff.
The German-speaking Jean-Marc Ayrault, who has strong contacts in Berlin, could be named prime minister later in the day.
Mr Hollande has picked an upscale hybrid Citroen as his official car and has had it fitted with a flat floor and a rail he can hold onto while standing up and waving to the public.
Aides said palace chauffeurs were frantically practicing driving the hybrid car without stalling it.