Agreeing a "road map" for the future of the EU, the German chancellor and French president agreed to tackle nationalists across the Union and looked forward to major treaty change which would allow more significant integration between the bloc's members.
French President Emmanuel Macron has appointed a conservative prime minister in a move to broaden his political appeal and weaken his opponents before parliamentary elections in June.
"From the German point of view, it's possible to change the treaty if it makes sense", she said.
"I am happy that we can work together on a common roadmap for the European Union and the Euro Zone", he said.
Speaking to BBC Radio 4's Today programme, Dr Ammon said: "We are happy to have a new star born in Europe, and that is Emmanuel Macron".
"The entire world is changing and we declare that we have exhausted ourselves once and that's it for our entire lifetime", she said. She said she was personally prepared to make the case for such a change.
And, despite the smiles on Monday, Mr Macron has yet to prove himself.
But the proposals have sent alarm bells ringing in Berlin, and initial relief about his victory against far-right leader Marine Le Pen have also given way to fears about his reform plans.
Macron's party announced a list of 428 candidates, a lot of them political unknowns, last Thursday to fight the parliamentary elections.
Macron is also working Tuesday to form a government after naming low-profile, center-right Edouard Philippe as prime minister.
"I told myself that the situation we were in was so unique that we should try something that had never been tried before", Philippe, a lawmaker and mayor of the port city of Le Havre from the center-right Republicans, said in comments broadcast by TF1 television.
Forces of division have been closing in on Le Pen since her electoral loss to centrist Emmanuel Macron, but she dismissed the notion that there were links between her loss and a series of events widely seen as potentially weakening her party.
French far-left leader Jean-Luc Melenchon, who won almost 20% of the vote in the first round of the presidential election, also reacted with hostility.
Merkel has hailed Macron's win as a blow for populism.
Mr Macron previously met Mrs Merkel when he visited Berlin in March as a candidate. While Germany's economy - Europe's largest - has been performing well in recent years, France's has stalled.
For the moment, she will be happy to see Macron live up to his promises of reform, especially at home where public spending needs to be brought under control and the labour market freed up.
She built a solid relationship with Mr Macron's predecessor, Socialist Francois Hollande, despite their political differences - notably with their joint effort to secure an accord to calm the fighting in eastern Ukraine in tense talks in Minsk, Belarus, in 2015.
There was a warm welcome for the new French president both from Angela Merkel and - unusually - a crowd singing and dancing outside the chancellory.