Lufthansa had scrapped 929 flights on Monday, grounding 113,000 passengers as cabin crew expanded their strike.
The strike has hit Germany's biggest airport of Frankfurt as well as Düsseldorf and the southern transit hub of Munich.
The action, in its third day, is expected to last a week, becoming the longest in Lufthansa's history as both sides fail to agree on cost cuts.
Nicoley Baublies, who heads the UFO flight attendants' union, hit out at Lufthansa saying it had “not once tried to get in touch” since negotiations broke down last Thursday.
Lufthansa however said it was “ready to resume discussions at any time”.
Lufthansa presented a new offer to the union on Monday evening, with improved bonuses and retirement provisions.
“In order that our customers are not penalised by the effects of this strike, we have decided to improve our offer, Lufthansa's head of personnel, Bettina Volkens, quoted as saying in a company statement.
UFO responded by saying its leadership would examine the new offer but added that “it changes nothing regarding the strike for November 10.”
The dispute over pay and early retirement provisions dates back to December 2013, when the company decided to embark on cost cuts in the face of intense competition from low-cost carriers.
The union is demanding that the current system of early retirement provisions remain unchanged, but Lufthansa has argued that those measures are too expensive.
UFO announced that the strike would continue Tuesday at the three affected airports, the biggest in the country.
However Lufthansa management said that nearly all internal and European flights would go ahead along with “some” long-haul flights.
Despite the industrial dispute, Lufthansa last week said it was raising its full-year forecasts after low oil prices and positive passenger numbers lifted profits in the third quarter.