Hollande said Germany and France would "put all ideas and all proposals on the table" to promote economic growth in Europe, France 24 reported Tuesday.
"Everything has to be looked at anew by everyone," Hollande said.
Hollande and Merkel said again they hope Greece can remain in the eurozone.
"I hope that we can say to the Greeks that Europe is ready to add measures to help growth and support economic activity so that there is a return to growth in Greece," Hollande said.
Hollande and Merkel are to meet again May 23 and in late June at a Council of Europe summit.
"It will be very important that Germany and France present their ideas together at this summit," Merkel said.
Hours after being sworn in, as he headed for Berlin, Hollande was forced to turn back to Paris after his plane was struck by lightning. Hollande swapped planes and renewed his journey.
"We don't think the same on everything," Hollande told French television Monday ahead of his Tuesday swearing-in. "We'll tell each other that so that together we can reach good compromises."
Hollande campaigned on a vow to renegotiate a German-inspired EU treaty that focuses on austerity and debt limits among eurozone countries, promising to add provisions promoting economic growth. Germany could not "decide for all of Europe," he said. He also called on the European Central Bank and the European Investment Bank, the EU's long-term lending institution, to play more active roles in stimulating demand.
Merkel, a conservative Social Democrat, has said the treaty, already ratified by numerous European countries, can't be touched, and it is wrong to use government money to boost the economy.
She told a news conference Monday she saw "no conflict between solid budgetary policy and growth."
Hollande -- in response to a growing democratic revolt in Europe and a deepening recession in Greece, Spain and Portugal -- was likely to urge Merkel to lower interest rates for those countries, or give them and more time to pay off debt, or extend beyond 2013 when they must reduce their deficits to 3 percent of gross domestic product, The New York Times reported Tuesday.
He may even push for a restructuring of the rest of Greek debt, the newspaper said.
Diplomats are already drafting a "political statement on growth" that can be tacked on to the EU treaty that is expected to include measures that will readjust fund targets, the Times said.
S. Carolina GOP Governor Nikki Haley breaks wood with hands [VIDEO]
'Duck Dynasty's Phil Robertson on indefinite hiatus after anti-gay remarks