But the move toward a solution won't stop major disruptions in the flight plan expected to last until Friday.
The strike was lifted at midnight (2300 GMT on Monday), and talks were expected resume "immediately and without conditions" a joint statement said.
The renewed negotiations avert a potentially disastrous planned four-day strike by about 4,000 members of the Cockpit pilots' union.
Lufthansa, Europe's biggest airline by passenger numbers, had asked a Frankfurt court to prevent the pilots strike from continuing past its first day, calling the action "disproportionate."
On Tuesday morning Lufthansa spokesperson Klaus Walther told broadcaster ZDF that the company expected a speedy agreement.
“We are optimistic that it will be successful, we're ready for it,” he said, adding that an agreement would likely be reached by March 8 after the strike by pilots to press demands over job security and pay issues.
“Not a single job at Lufthansa has been relocated abroad and it's not planned,” Walther said. “We can relieve the pilots of this fear.”
The Lufthansa spokesperson added that the company is also “gladly ready to discuss a contractual job guarantee.”
Meanwhile unions representing 16,000 Lufthansa cabin crew threatened to follow the pilots' lead if the firm failed to come to terms with them as well. A wage contract with cabin crew expires on February 28, but management has failed to make a new offer and is refusing to hold talks, UFO union spokesman Nicoley Baublies said.
Lufthansa, like most rivals, is reeling from upheaval in the global airline sector. Worst hit by the strike were the airline's hubs in Frankfurt, Europe's third biggest airport, and Munich.
Lufthansa Cargo, one of the world's biggest freight carriers, and the firm's low-cost subsidiary Germanwings were also affected, though the cargo unit said more than 85 percent of its capacity had been covered on Monday.
Cockpit spokesman Jörg Handwerg nonetheless told AFP the strike had been "a great success." The union says it is trying to defend the terms of a contract signed with Lufthansa in 2004.
"We have a contract and Lufthansa is breaking it" by boosting the number of flights operated by subsidiaries with lower costs, Handwerg explained. Starting pilots at the parent group earn an annual pre-tax wage of €60,000 ($81,600 dollars) according to its website, and one with more than 15 years with the airline told AFP his pay was double that.
With the strike announced last week and the airline informing passengers in advance, the situation at Frankfurt's airport on Monday had been orderly since many travellers had made other arrangements. But others had to scramble, including Nigerian Hope Odia, 41, who was trying to make it back home for his father's funeral, while his nephew Chester Ade waited to see if something could be arranged.
"This is terrible," Ade said. "The stress is getting greater and greater."
European airlines have been fighting for survival meanwhile as they battle with the triple challenges of low-cost airlines poaching customers, soaring fuel costs and the worst global recession in decades.
Lufthansa has nonetheless bulked up during the crisis via the purchase of a number of smaller carriers such as BMI, the former British Midland, and Swiss, formerly Swissair, and by creating its own subsidiary in Italy.
In France, a planned strike by air traffic controllers was set to disrupt a quarter of the flights from Paris' main airport Charles de Gaulle on Tuesday, authorities there said.