"We have decided to pursue our claims for compensation via the courts," said chief executive Hartmut Mehdorn.
"We have previously tried to find a solution that is acceptable for both sides via intensive negotiations with the airport.
Unfortunately, we have not succeeded and so we now see filing a suit as the only way to defend our interests," Mehdorn said.
Air Berlin said it could not yet fully gauge the losses incurred by the delays, but that so far these had run into the "double-digit millions" of euros.
The carrier complained that it had expanded its services to and from the German capital by an extra 230 flights a week.
"These must be carried out at Tegel airport, where there is not sufficient infrastructure to cope," it argued.
Most recently expected to open on June 3 this year and replace the city's current two hubs, Schönefeld and Tegel, the Berlin-Brandenburg International Airport (BER) was delayed indefinitely in May after problems over fire safety.
The planned opening date is now October 27, 2013.
The scandal has dented the popularity of Berlin Mayor Klaus Wowereit, accused of incompetence and underestimating construction problems.
The country's top two airlines, Lufthansa and Air Berlin, have expressed outrage over the repeated delays to the project, which is next to Schönefeld in the southeast of the city.
Lufthansa said it had not yet decided whether to claim damages and declined to estimate a possible sum if it should.
Berlin's airports are not the country's busiest, with Schönefeld and Tegel combined welcoming around 24 million visitors a year - less than half the 56 million passengers serviced at Frankfurt airport in western Germany.
But the new airport, to be named after former chancellor Willy Brandt once opened, is intended to accommodate the sharp rise in air traffic to the region seen since the fall of the Berlin Wall and German reunification.
It is due to service around 27 million passengers a year.