In a solemn ceremony at the German Bundestag, parliament speaker Norbert Lammert said the program was the first to use gas to murder those considered "unworthy of living" and served as a "trial run for the Holocaust".
"It became the model for the mass murder that would follow in the Nazi extermination camps," he said in a speech attended by Chancellor Angela Merkel and relatives of victims.
Adolf Hitler's euphemistically named euthanasia program, in which doctors and scientists actively participated, sought to exterminate the sick, the physically and mentally disabled, those with learning disabilities and those considered social "misfits".
Between January 1940 and August 1941, doctors systematically gassed more than 70,000 people at six sites in German-controlled territory, until public outrage forced them to end the overt killing.
But tens of thousands more died across Europe until the war's end in 1945, through starvation, neglect or deliberate overdoses administered by caregivers.
Many also underwent bizarre medical experiments and forced sterilisations because of their supposed genetic inferiority.
In Friday's ceremony, an actor with Down's syndrome read out a letter from one of the victims, Ernst Putzki, who wrote to his mother in 1943 describing the inhumane conditions at the institution where he was being held in Weilmuenster, western Germany.
"Death from starvation is hard on our heels and no one knows who will be next," he wrote.
"Before, the people here were killed more quickly and their bodies were taken for burning at dawn. But this was met with resistance from the locals.
"So now we are simply left to starve."
Putzki died in January 1945, officially of pneumonia.
Ceremonies are held around the world each year on January 27 to remember the World War II victims of the Nazis.
The day coincides with the anniversary of the liberation of the Auschwitz-Birkenau death camp in Nazi-occupied Poland by Soviet troops in 1945.
Of the six million Jews killed in the Holocaust, one million were murdered at Auschwitz, mostly in its notorious gas chambers, along with tens of thousands of others including Poles, Roma and Soviet prisoners of war.
