Germany's flagship airline cancelled 900 flights on Wednesday and 912 flights for Thursday, hitting some 200,000 passengers.
It is the 14th strike since April called by the Vereinigung Cockpit pilots union.
Lufthansa urged VC to work towards a resolution rather than an escalation.
However, union spokesman Joerg Handwerg said: "Lufthansa management has shown no sign that it is willing to move and has not provided an offer that could serve as a basis for negotiations."
Pay talks between VC and the German carrier broke down earlier this month, and Lufthansa said the union had "consistently rejected the offer" of mediation.
The union is calling for a 3.7% pay rise for 5,400 pilots dating back to 2012. Lufthansa, which is facing increasing competition from budget rivals, offered a 2.5% increase over the six years until 2019.
"Cockpit's demand for a pay rise... goes far above what other groups of employees have received. It is incomprehensible why the union is seeking the highest salary increase for the best paid group of employees," said Bettina Volkens, Lufthansa's human resources chief.
The airline tried twice on Tuesday to seek a court injunction to prevent the walk-out, which was due to last two days.
Lufthansa, led by chief executive Carsten Spohr, insists that despite making a profit in 2015, it has no choice but to cut costs to compete with leaner rivals such as Ryanair on short-haul routes and Emirates on long-haul flights.
He has said that he expects the strike to cost between â‚¬7m and â‚¬9m a day.
Mr Handwerg said: "Let me make it very clear that going on strike gives us no pleasure. We are sorry for the passengers and we cannot understand why Lufthansa is unable to make a negotiable offer."
A Lufthansa pilots strike that halted hundreds of flights appeared to be intensifying after the union called for the action to be extended to Friday.