* Repeated postponements hit German reputation for efficiency
* City's mayor blamed by many for airport's fifth delay
* Under fire, Wowereit cedes leadership of supervisory board (Updates with Wowereit comments from news conference)
By Erik Kirschbaum
BERLIN, Jan 7 (Reuters) - Berlin Mayor Klaus Wowereit stepped down on Monday as head of a board overseeing the building of the city's new international airport after yet another delay in the project dealt a fresh blow to Germany's reputation for efficiency.
Wowereit, a focal point of criticism due to delays in opening the 4.3-billion-euro ($5.6 billion) airport, bowed to the pressure and gave up the supervisory board chair to Brandenburg state Premier Matthias Platzeck. The airport is jointly owned by Berlin, Brandenburg and the federal government.
But Wowereit told a news conference he would not resign as mayor, despite calls for him to step down, due to the debacle over Willy Brandt International Airport, which was originally planned to open in 2008.
Already 20 years in the planning when construction began in 2006, the airport was then set to open in 2011. That was pushed back to June 2012, then to March 2013, then to October 2013 and now to some point after 2014.
"I'm going to be guarded about picking a date now," Wowereit said. "That it would be difficult to meet the target we had for this year was already known up and down the country."
The delays, caused mainly by problems with the fire-safety system, have turned the airport and its city into a nationwide butt of jokes. Authorities fear the latest hold-up could harm the global reputation of German engineering.
Tegel airport - one of three in the German capital that Willy Brandt International is meant to replace - was built in just 90 days during the Cold War.
Sixty years after that feat, the protracted struggle to open the new airport has exposed the inefficiencies of a country weighed down by regulations and layers of bureaucracy.
Construction only began in 2006 after a tortuous 15-year planning and approvals process for the air hub in the southeast corner of Berlin.
Wowereit has been mayor since 2001. He became a national celebrity by coming out as gay during that election campaign just as one newspaper was planning to expose his sexuality.
Wowereit, a Social Democrat, has come under fire over allegations that he covered up news of the latest delay for the last three weeks, which prompted calls for his resignation that he later dismissed.
"Wowereit has withheld information about new problems at the airport and he's a liability," said Ramona Pop, a leader of the opposition Greens in the city-state assembly. She said the assembly should vote him out. "He's harming Berlin's interests."
The Greens' national co-leader, Juergen Trittin, intervened to tell Wowereit to step down: "It's over, Klaus."
But Wowereit won a potentially vital lifeline from his own party on Monday.
"Why should he resign? I can't see any reason for that," said the chairman of the Social Democrats (SPD), Sigmar Gabriel.
"If the technical experts say the airport opening has to be delayed, what else can the supervisory board chairman do?"
The calls for Wowereit to go are not likely to lead to his exit as the SPD has slumped in Berlin in opinion polls and the party could end up losing power in a snap election. There is also no heir apparent. But pressure on Wowereit is growing in the media and his standing in opinion polls has suffered.
At the height of his national popularity in 2006, Wowereit was one of only a handful of SPD state leaders capable of winning their elections and many saw him as a future chancellor.
Wowereit, 59, took over a city deeply in debt and struggling to overcome decades of Cold War divisions. With high unemployment and low wages, Berlin was also struggling to find its place in reunited Germany.
"Berlin is poor but sexy," Wowereit once said, giving the city a hip slogan that stuck and helped him win re-election three times. That image helped lure film and music companies as well as tens of thousands of artists and writers to Berlin even as the city's jobless rate fell and the cost of living climbed.
The new airport is named after Willy Brandt, the late former West German chancellor and Nobel Peace Prize laureate who also served as mayor of old West Berlin. ($1 = 0.7666 euros) (Reporting By Erik Kirschbaum, Editing by Gareth Jones and Mark Heinrich)