"There is a common conviction that we cannot only deal with Britain's exit (from the EU), but instead that we must above all think about how we can deepen the existing European Union and especially the euro zone", she added.
The two leaders said Mr. Macron's victory in France's presidential election could breathe new life into the Franco-German relationship, which has always been the motor for deepening the binds of European Union member states.
French President Emmanuel Macron chaired the first meeting of a cross-partisan government on Thursday, uniting right-wingers, left-wingers, old hands and new faces in a team whose first goal is to win parliamentary elections in June.
She says: "A European Union that behaves this way would be vulnerable from every corner of the world".
Merkel will be buoyed by his remarks as she basks in the glory of winning three consecutive regional elections, in Schleswig-Holstein, Saarland and the crucial state of North Rhine-Westphalia - which is the most populous state of Germany and includes Dusseldorf, Bonn, Cologne, Dortmund, and Essen.
Underlining concerns over Macron's proposals, Germany's biggest selling daily Bild warned that before seeking deeper European Union integration, "France must once again be at the same level as Germany politically and economically".
Macron, a centrist, was elected last week, defeating anti-EU, anti-immigrant candidate Marine Le Pen.
During his campaign, Macron had thrown up ideas on reforming the eurozone, noting that the currency bloc can not go on as it is if it wanted to avoid falling prey to protest and populism.
His candidacy and victory was embraced by Merkel, who said during the May 15 news conference that, while treaty changes are not an immediate subject of discussion, she is open to the idea.
"From the German point of view, it's possible to change the treaty if it makes sense", she said.
Merkel called for a "new dynamism" in German-French relations, saying that the two countries' interests are closely tied together.
And in France, opponents of such reforms have already vowed to launch street protests against any attempt by Mr. Macron to liberalize France's highly regulated labor market.
It is Le Maire who probably matters most.
Jean-Yves Le Drian, a 69-year-old former defense minister under then President Francois Hollande, stays on in Macron's government as foreign minister and Europe minister.
The president only told journalists that Philippe was part of a new French political landscape that he was promoting.
Asked about the crowds who cheered his arrival, he said it showed that European citizens remain committed to the EU and that he wants to be cheered again - five years from now at the end of his term - because governments have produced results.
Earlier Monday in Paris, Macron named centre-right lawmaker Edouard Philippe as prime minister in a further effort to splinter the country's traditional parties and redraw the political map.