Gauck said people across Germany, which lost 72 citizens, are still coming to grips with the March 24 crash. The second-biggest group of victims was from Spain, which lost 51 citizens.
Prosecutors have said co-pilot Andreas Lubitz deliberately crashed the plane into the French Alps on the way from Barcelona to Duesseldorf, killing all 150 aboard. They are still trying to determine why.
"But we do know that his relatives also lost on March 24 a person whom they loved, who leaves a void in their lives, in a way for which they can find as little sense as all of the others' relatives," Gauck said.
"Maybe that is what appalled us so much, the senselessness of what took place." The steps to the altar were covered with 150 lighted candles, one for each person who died.
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Lufthansa carried a livestream on its website and took out full-page advertisements in many of the country's leading newspapers expressing sympathy. Flags were ordered flown at half-staff around the country.
Cardinal Rainer Maria Woelki, the archbishop of Cologne, told victims' relatives that words alone were too weak to give them any solace, but that they should take comfort in the numbers of people at the memorial service, and those following it online or on television.
"You are not alone in these hours of loneliness," he said.