Travelling to the German capital to meet the veteran leader in his first official trip overseas, Macron used the opportunity to call for a "historic reconstruction" of Europe.
Merkel said that, from Germany's viewpoint, treaty change would be possible, adding: "I would be ready to do this, but first we will work on what we want to reform". Merkel cited the urgency to act at a "critical moment" as the European Union confronts a series of crises in addition to Britain's exit.
During his campaign, Mr Macron had thrown up ideas on reforming the euro zone, noting that the currency bloc can not go on as it is if it wanted to avoid falling prey to protest and populism.
Macron's defeat of far-right candidate Marine Le Pen in a run-off vote this month was greeted with relief by pro-EU political forces rattled by a surge in populist, Euroskeptic sentiment across the continent, including last year's Brexit referendum vote approving Britain's departure from the bloc.
He also announced he would initiate "deep reforms" in France in order to tackle unemployment.
Merkel said they had "a common understanding that we can't just focus on Britain leaving the EU but that, first and foremost, we have to think about how we can deepen and crisis-proof the European Union, and especially the eurozone". While Germany's economy - Europe's largest - has been performing well in recent years, France's has stalled.
Hollande's five years in power were plagued by a sluggish economy and bloody terror attacks that killed more than 230 people.
"We agreed that we want to develop a road map for the European Union's medium-term perspectives". Alain Juppe, a former prime minister, called Philippe "a man of great talent" with "all the qualities to handle the hard job".More news: Arsene Wenger praises devilish Alexis Sanchez after brace against Sunderland
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It's a delicate balancing act, as Macron tries to redesign French politics by borrowing ministers from left and right and new faces.
Some in the party have argued in favour of an alliance with Macron.
Around 20 MPs on Monday issued a statement urging the Republicans and centre-right UDI to "accept his outstretched hand", saying the right needed to "take the full measure of the political transformation taking place before their eyes".
"We know that in the world in which we live in it's not the president who imposes foreign policy, but foreign policy that imposes itself on the president", said Francois Heisbourg, a Macron adviser and chairman of the International Institute for Strategic Studies.
"I have never defended (the idea of) Eurobonds or the mutualisation of existing debt in the euro zone", he said.
"We can give the entire [European] construct a new dynamic", Merkel said, adding Europe could only progress with a "strong France" within.
The delay was to allow checks to be made on their tax status "whereas the law stipulates that this check only needs to be done after they are named", the presidency said.
The statement was a clear nod to Germany, which has been vigorously opposing the idea of taking responsibility for the debts of weaker, crisis-hit European Union member states.