Mrs Merkel has praised Mr Macron's embrace of European unity but has offered few concrete details about the way forward for German-French relations. But her ruling coalition is at odds over how to respond to his calls for closer European Union integration.
Merkel said that Germany needs France to succeed, emphasizing that "Europe will only do well if there is a strong France".
The French president added that France was the only large European Union country, which failed to deal with unemployment in 30 years. Monday's meeting was an effort to inject some dynamism into the partnership.
The pair said they are both prepared even to implement treaty changes if needed.
Ahead of his visit, Macron's ideas on reforming the eurozone - including setting up a separate budget, legislature and finance minister for the currency bloc - had sparked scepticism in Berlin.
Merkel's conservatives sought to portray Kraft's government as slack on security, and also assailed what they said is regional authorities' poor handling of education and infrastructure projects.
She also made her most positive comments yet about eurozone reforms mooted by Mr Macron, saying it may be possible to change European Union treaties as would be required to enact them.
After a private meeting with Hollande and his first speech as president, Macron headed up the rainy Champs Elysees avenue in an army vehicle, waving to small crowds of wellwishers.
Merkel, receiving her fourth French president since taking office nearly 12 years ago, told the freshly elected Macron that Germany would be willing to consider changing European Union treaties if necessary.
The 39-year-old former investment banker and economy minister was inaugurated on Sunday as the 25th President of France and also the youngest in the nation's history in a ceremony at the Élysee Palace.
Macron also soothed German concerns over the mutualising of "old debt" between eurozone countries, saying he does not favour the idea of so-called eurobonds, but adding that he was open to sharing future burdens.
Some could be replaced after next month's parliamentary election, depending on how many seats Macron's fledgling Republique En Marche (REM) party wins.
"There are several areas in which we can cooperate in the short term", he added. "We need more trust, much more trust and more specifically, results".
'That is going to be easier said than done, it appears, with USA production running at its fastest pace since August 2015 and data yesterday confirming that Chinese growth momentum continues to moderate, ' ANZ strategists wrote in a daily note.
Macron, the fervently pro-European centrist sworn in as head of state on Sunday, in keeping with tradition made his first trip overseas to Berlin, its power couple partner at the heart of the European project.
Mr Macron is the conservative Mrs Merkel's fourth French president in almost 12 years as chancellor.
German media, including the influential tabloid Bild and news magazine Der Spiegel, have recently drawn attention to the danger of Macron's presidency costing Germany more money.