Six days of industrial action over the past week have forced Lufthansa to cancel 4,461 flights, grounding more than half a million passengers.
On Wednesday, around 98,000 customers were affected by 890 cancellations.
The firm said it would offer pilots a 4.4-percent pay rise, spread over two years and not linked to any other conditions, as well as a one-off payment.
“We want to urgently avoid any further damage to our company,” Lufthansa board member Harry Hohmeister said in a statement.
Airline bosses made a similar pay offer at the weekend but tied it to changes to pensions which pilots deemed unacceptable, their union Vereinigung Cockpit said.
Pilots walked out again on Tuesday – for the 15th time since spring 2014 – after talks during a two-day pause in strikes had failed to find a solution.
Wednesday's strike extended to some long-haul services after only short-haul flights were affected on Tuesday.
The airline has sought to limit the impact of the strike by introducing an emergency timetable.
But each day of the walkout costs the firm between €10 and €15 million, a spokesman told AFP.
Earlier on Wednesday, Lufthansa said 40 further flights would be cancelled Thursday due to the after-effects of the strike – even as pilots returned to work.
Other airlines in the group, including Eurowings, Swiss, Austrian Airlines and Brussels Airlines, are not affected and are running normal services.
Lufthansa has dealt with repeated high-profile strikes over the past two years as it pushes to cut costs in the face of stiff competition from low-cost European rivals like Easyjet and Ryanair, as well as from higher-end Gulf carriers.
In July, the airline reached a deal with cabin crew covering pay, working conditions, jobs guarantees and a no-strike agreement lasting until 2021.
Their union UFO had staged the firm's longest-ever strike in November 2015, grounding 4,600 flights with a seven-day stoppage.
The pilots' battle has lasted longer, with Cockpit complaining members had seen no wage increases in five years despite Lufthansa booking healthy profits.
They have been demanding a pay rise of an average of 3.66 percent per year, retroactive for the past five years.
Lufthansa has always insisted that it pays pilots better than its competitors.
A pilot in the top seniority category can earn more than €22,000 euros per month.
The airline said last month that it expects its annual earnings before interest and tax will reach “approximately the previous year's level” of €1.8 billion.