Merkel had branded an original French idea as divisive because it envisaged a grouping of Mediterranean rim states, including its former North African colonies, drawing on EU funds while sidelining non-Mediterranean EU countries such as Germany.
"You will see that we have found a compromise on this Mediterranean Union, which will not exclude anyone," Sarkozy said at a joint news conference with Merkel in the northern German city of Hanover.
He did not elaborate, but Merkel said the Mediterranean Union would be a project involving all EU member states, and both leaders said they would present details to partners at a coming EU summit.
France had already watered down the project, assuring European Union partners it would complement rather than replace the existing EU-Mediterranean framework, and symbolically renaming it a "Union for the Mediterranean".
"It doesn't matter to me whether it's called Mediterranean Union or Union for the Mediterranean," Merkel said, "What's important is that this is a project of EU states."
The French president had initially aimed to launch the Union at a Paris summit on July 13-14, with the Mediterranean states attending the first day and other EU states joining to bless the initiatives on the next, the national holiday Bastille Day.
But officials say France, which takes over the rotating EU presidency in July, now favours switching those dates, starting with the meeting of all EU states.
CONFLICTS
Merkel and Sarkozy have differed over a series of economic and foreign policy issues since the French president took office last May, including the independence of the European Central Bank, nuclear energy contracts and industrial policy.
Monday's meeting, at the opening of the CeBIT trade fair in Hanover, came after France had cancelled two high-level meetings between French and German leaders.
In a speech earlier on Monday, Sarkozy justified his policy of defending "national champions", which has raised eyebrows in Germany, and said Paris and Berlin differed over economic policy, including the role of the state in the economy.
But the two leaders emphasised unity at their joint news conference, saying strong relations between France and Germany were important for the entire European Union.
"It's obvious that we always find agreement when it matters," Merkel told the news conference, smiling.
Sarkozy added: "What's important is not to have problems but to find solutions."
Merkel said Germany would support France on issues including the fight against tax evasion, when Paris takes over the EU presidency.
"We want to further develop policies against tax havens and will support France in this during the presidency," she said.
Germany has spearheaded a crackdown on tax havens, targeting hundreds of Germans who may have evaded taxes by parking money in Liechtenstein.