Airline also raises fuel surcharges
Lufthansa said premium travel was still falling rapidly although economy had steadied over the last few months.
The airline said in a presentation at its Investors' Day that told both traffic and its load factor had fallen by 4.4% in May.
During the current crisis, Lufthansa said it had cut capacity by 2.6% and retired 23 planes. There are likely to be further capacity cuts later this year.
The airline also announced today (June 25) that it was raising its fuel charges.
The presentation comes after the German flagship said it would not be posting a profit this year as expected unless it imposed further cost cuts and surcharges.
The airline said its fuel bill for the year was likely to rise from a forecast in April of €3.4bn to €3.55bn.
Oil prices have risen by about 50% this year after dropping from a high last summer of $145 a barrel. They are currently around $70 a barrel.
Lufthansa's chief financial officer Stephan Gemkow said fuel prices were a challenge both to the company and to the industry.
The airline said it was increasing its fuel surcharge on domestic and European flights by €3 to €23 per flight. In future flights to Israel, Lebanon, Jordan and North Africa would be counted as European services.
On long haul flights, the standard surcharge of €82 would be staggered. Middle East destinations would be charged €77 per leg, North America and India €82and South America, Central, West and Southern Africa, South East Asia and the Far East €92.