Germany has held the EU's rotating presidency since January.
Erdogan told a German magazine shortly before his two-day visit that Germany could have done more to push on with Turkey's EU membership talks during its leadership of the bloc.
"I seriously expected more from Germany," Erdogan was quoted as telling Der Spiegel news magazine.
"We would like a clear idea of a date, a roadmap, a calendar for negotiations," he said, adding that "2014 or 2015" would be a realistic and possible date.
Erdogan struck a conciliatory note on Sunday, saying: "One cannot attack a lady. We are on a long, narrow road and we have to be patient."
He said, however, that his criticism had been "legitimate".
Merkel said on Sunday that the EU could open two more sessions of talks on Tukey's membership before the German presidency ends in July.
But she said Turkey must open its ports to shipping from Cyprus.
|Erdogan said he had "expected |
more from Germany" [Reuters]
"We are looking ahead but the outcome of this process remains open," she said, adding that it is "important that Turkey normalises ties with Cyprus".
The EU relaunched talks on Turkey's membership at the end of March after a long hiatus caused by Ankara's refusal to respect trade obligations to Cyprus under a customs agreement with the EU.
Turkey has refused to open its ports and airports to Greek Cypriot traffic until the EU lives up to its pledge to end the isolation of the Turkish Cypriot territory in the north of the Mediterranean island.
Turkish northern cyprus is recognised only by Ankara.
Merkel's coalition government supports Turkish EU membership but the German leader has told her own Christian Democrat party that she personally opposes full membership.
Instead she favours a "privileged partnership" for Turkey within the bloc.
Since becoming chancellor, she has stuck to the line agreed to with her coalition partners, the Social Democrats, to continue talks with Turkey.
Merkel and Erdogan met before opening the Hanover Trade Fair where Turkey is the guest nation.