Mr Winkelmann said: "This day is costing us several million euros. A stable operation is mandatory for these negotiations to succeed".
Lufthansa's low-priced subsidiary Eurowings, which is renting aircraft as well as pilot and crew from Air Berlin, has also been forced to cancel some flights.
"At the moment more than 110 flights have been canceled, with about 12,000 passengers affected", the spokeswoman said.
An estimated one-sixth of the airline's 1,500 pilots called in sick on Tuesday, which is likely to represent one-third to one-half of the total rostered to work. "That's the only way we can secure as many jobs as possible".
Air Berlin said once it had received the offers from potential investors on Friday, it hoped to reach a decision by September 21.
The airline has been struggling for some time and over the past two years has announced losses amounting to 1.2bn euros (£1.1bn).
Frank Kebekus, the company's chief representative, said the events "seriously endanger the entire insolvency proceedings under self-administration" and that if the situation did not change quickly, "we will have to cease operations and thus any restructuring efforts". That is crucial in order to bring talks with investors to a successful conclusion. The previous owner Etihad announced Air Berlin's insolvency in August, prompting uncertainty over its future and the search for a buyer.
Germany's giant services sector union Verdi expressed solidarity with the absent pilots and warned that more workers could call in sick.
In the meantime, the airline has been kept aloft by a hastily-agreed 150-million-euro loan from the German government.