About 800 flights per day will be canceled over a four-day period, as pilots at Deutsche Lufthansa
The strike, which started at 2300 GMT on Sunday, or midnight local time, is the biggest in the German flag carrier's history, according to the airline.
Passengers are being rebooked on flights operated by rivals and Lufthansa subsidiaries or have to switch to trains for domestic travel.
Monday was also the final day of a cabin crew strike ballot at Lufthansa's rival British Airways
Lufthansa's pilots voted for the strike on concerns that the company could try to cut staff costs by shifting jobs to foreign subsidiaries such as Austrian Airlines
Over the weekend, the pilots' union offered new negotiations, but Lufthansa said it would not resume talks unless the union dropped demands for what it saw as undue influence on managerial decisions.
We are still prepared to resume negotiations, without preconditions, but then (pilots union) Vereinigung Cockpit needs to be prepared as well to hold talks with no conditions and drop its catalog of demands, which cannot be fulfilled and is legally inadmissible, a Lufthansa spokeswoman said on Monday.
The union had also said late on Sunday that it was in principle prepared to resume talks, but said that Lufthansa had not been prepared to give up some of its own demands.
Lufthansa has said the strike will cost it about 100 million euros ($135 million) in cash, in addition to lost ticket sales and possible damage to its reputation.
Germany's economic recovery stalled at the end of 2009, and workers are becoming increasingly concerned that they could lose their jobs.
They are looking to employers to promise job security in exchange for concessions on pay, as carmaker Volkswagen has.
Engineering sector workers have also accepted moderate wage increases to help boost employment prospects.
(Reporting by Maria Sheahan; Editing by Mark Trevelyan and Sharon Lindores)