Steinmeier called the European Union "a successful project of peace and stability" and said that there was a "strong desire" within the bloc to defend and strengthen it.
"I think it is absolutely clear that we are in a situation in which neither hysteria nor paralysis are permissible," he said.
"We must not rush headlong into hectic action, pretending we had all the answers. But we must also not fall into depression or inaction after the British decision."
Steinmeier hosted Ayrault, the Netherlands' Bert Koenders, Italy's Paolo Gentiloni, Belgium's Didier Reynders and Luxemburg's Jean Asselborn in a lakeside villa north of the city centre.