BERLIN — Klaus Wowereit, the party-loving mayor of Berlin who once characterized his city as “poor, but sexy,” will step down in December after more than 13 years presiding over the German capital, he said on Tuesday.

While the timing of his announcement was something of a surprise, Mr. Wowereit had seen his star fall rapidly since a new city airport has swallowed billions of euros in construction costs and has fallen four years behind schedule.

Even the latest start date of 2016 is uncertain after a cascade of reports about corruption, shoddy planning and poor construction at the airport. It has been anything but the showcase of an efficient, reunited 21st century Germany originally envisaged.

The airport was “a bitter defeat,” his greatest in office, the mayor said at a news conference. But he indicated his pride at presiding over Berlin as it became what he called, in English, “the place to be.”