While not ruling out further action, the union said that any strikes would be announced 24 hours in advance.
Lufthansa said it expects flights to operate largely as scheduled on Sunday.
A pay offer to pilots made by Germany's Lufthansa on Friday in a bid to end a three-day strike has been rejected by the pilots' union, Cockpit.
Pilots had been threatening to extend the strike beyond Saturday, raising concerns among investors at the growing cost to the company and the wider impact on Europe's largest economy.
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Initially, the union said the strike would last two days, but extended it to Friday and again to Saturday as negotiators failed to resolve the impasse.
A Lufthansa spokesman said the flight plan was otherwise "more or less" normal, and that if Cockpit did not call another strike for Monday, operations would run completely as usual as the week starts.
It also offered to hire about 1,000 new pilots in the coming five years and seek third-party mediation on other outstanding issues.
Last week Lufthansa had to cancel almost 2,800 flights during a four-day strike from Wednesday that affected more than 350,000 passengers, the 14th walkout in a dispute that since early 2014 has cost the carrier hundreds of millions of euros.
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Bettina Volkens, head of human resources at the airline, said the changes would help the airline save money.
A Lufthansa pilot in the top seniority category can earn more than 22,000 euros ($23,000) per month.
Lufthansa is losing €10m a day due to cancelled flights. The airline had previously offered a 2.5% pay hike. That is fewer than on previous days, when union members also hit short-haul flights.
The top-selling daily Bild says the strike is costing Lufthansa some 10 million euros ($10.5 million) a day.
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