The strike - the 14th since April 2014 - has affected more than 315,000 passengers, with the airline forced to cancel 2,618 flights over three days.
The Lufthansa pilots are demanding a pay rise of an average of 3.66 percent per year, retroactive for the past five years.
Their union says pilots have endured a wage freeze over that time and suffered a "significant loss of purchasing power" due to inflation, while Lufthansa has made billions in profits.
The airline had offered a 2.5 percent wage hike, which the Cockpit union dismissed as "not even worth negotiating on".
Lufthansa's hub management board member Harry Hohmeister said Thursday it was "not possible" to meet the pilots' demand for a bigger wage hike.
"The starting point is that we already pay our pilots far better than our competitors," he said.
Then late Thursday the Cockpit union announced that the strike would continue for a fourth day on Saturday and would affect all the long-haul flights from Germany scheduled for that day.
Affected passengers can rebook their flights without charge or request rail travel vouchers, the airline said.
It has also reserved thousands of hotel rooms for stranded travellers, while camp beds had been set up at Frankfurt airport for passengers who do not have a valid visa to enter Germany.
Austrian Airlines and Swiss -- part of the Lufthansa group -- have tried to pick up some of the slack by expanding their service to Germany.
The Lufthansa group's other airlines - Germanwings, Air Dolomiti and Brussels Airlines - have also not been affected by this week's strike.
Bild daily said the strike costs Lufthansa some €10 million a day, in addition to the damage to airline's brand image.
Lufthansa has urged Cockpit to work towards a resolution rather than escalate the dispute but failed to win a court order to block the strike, as it had managed to do one year ago.
"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.
A pilot in the top seniority category can earn more than €22,000 per month.
Lufthansa has been battling a series of walkouts by both the pilots and cabin crew over the last two years, as it aims to bring down costs to survive competition from low-cost rivals such as EasyJet and Ryanair.
Lufthansa has responded by focusing on long-haul flights and catering to business and first-class passengers.
In July, it brought an end to the long-running industrial dispute with cabin crew through a deal on pay and working conditions, including a no-strike agreement and job guarantees until 2021.