FRANKFURT (Reuters) - Germany's biggest airline Lufthansa <LHAG.DE> has canceled 35 flights on Sunday as the fallout from a four-day strike by pilots over pay spilled into a fifth day.

The additional cancellations announced by the airline pushed the number of flights grounded since the walkout started on Wednesday to nearly 2,800, with more than 350,000 passengers affected.

"Almost all LH (Lufthansa) flights will operate according to schedule tomorrow. However, 35 flights canceled due to the strikes on the preceding days," the company said via Twitter on Saturday.

A spokesman also denied an unsourced report in Frankfurter Allgemeine Zeitung that said the airline had considered going insolvent to rid itself of the costly labor agreement with its pilots, which lies at the heart of the conflict.

Late on Friday, Lufthansa's pilots union rejected the German airline's latest pay offer but lifted the immediate threat of extending their strike beyond Saturday.

"We need a negotiable offer. Otherwise there can always be additional strikes," Joerg Handwerg, board member at pilots union VC, told Reuters TV on Saturday.

Lufthansa had offered to increase wages by 4.4 percent in two installments, as well as a one-off payment equal to 1.8 months' pay.

The union wants an average annual pay increase of 3.7 percent for 5,400 pilots in Germany over a five-year period backdated to 2012.

(Reporting by Christoph Steitz and Reuters TV; editing by David Clarke)