The parents of 16 students from the German town of Haltern accused Carsten Spohr of never speaking with relatives to apologise – a claim disputed by the airline.
The letter comes amid negotiations with Lufthansa, Germanwings’ parent airline, over compensation for the March 24 crash.
Prosecutors believe the Airbus A320 was intentionally crashed into a French mountain by co-pilot Andreas Lubitz, killing all 150 people on board the flight from Barcelona to Dusseldorf.
Lufthansa has offered around 100,000 euro (£70,000) per family, depending upon its size.
German lawyer Elmar Giemulla, who represents the Haltern victims, has said the offer is far too low and is seeking at least three times that amount.
In their letter, provided by Mr Giemulla, the parents, along with the fiancé and husband of the two teachers who were with the Haltern school group killed in the crash, said Mr Spohr talked to a lot of newspapers, “but you haven’t spoken with us”.
They added: “You saw us at the memorial service in Haltern and the memorial in Cologne. A couple of personal words would have shown us that you were not only there for the public, but also for us.”
They added that Lufthansa’s compensation offer “deeply insults us, and above all else our children”.
Lufthansa spokesman Andreas Bartels insisted Mr Spohr had made every effort to talk with families, and attended not only the services in Haltern and Cologne but had also been to Barcelona and twice to the crash site.
“Mr Spohr was in touch with many relatives and friends and family of the victims but it’s obvious that he was not able to be in personal touch with each and every one of the more than 1,000 relatives that we have,” he said.
Parents of the Haltern victims were among those he talked to, and he also sent a condolence letter apologising to all families, Mr Bartels added.
Meanwhile, a Lufthansa plane almost collided with a drone as it approached Warsaw international airport, Polish officials have revealed.
Warsaw airport spokesman Przemyslaw Przybylski said the incident occurred on Monday afternoon at around 4pm local time and the drone came within 300ft of the plane, which was arriving from Munich.
He said the near-collision occurred about three miles from the airport.
He added that police were investigating the incident to determine who operated the drone, which should not have been flying in that location.
Mikolaj Karpinski, of the Polish Air Navigation Services Agency, told the TVN24 broadcaster that the pilots immediately reported the drone to air traffic controllers, who redirected the plane.
Mr Karpinski said he considered the incident to be serious.
However, Lufthansa spokeswoman Bettina Rittberger was more hesitant about declaring the object a drone.
She said that “a black object appeared on the right side of the plane” at an altitude of 2,500ft and the crew “supposed that this object could be a drone”.