"For me there's no question that I share moral guilt," the 93-year-old former Nazi told the judges, admitting that he knew about the gassing of Jews and other prisoners.
"I ask for forgiveness," he said at the trial, which was attended by almost 70 Holocaust survivors and victims' relatives.
"You have to decide on my legal culpability," Gröning told the court in the northern city of Lüneburg near Hamburg.
Given the advanced age of most German war crimes suspects, Gröning is expected to be among the last to face justice, 70 years after the liberation of the concentration camps at the end of World War II.
He is being tried on 300,000 counts of "accessory to murder" in the cases of deported Hungarian Jews who were sent to the gas chambers, and faces up to 15 years in jail.
Prosecutors said Gröning served as an accountant, who sorted and counted the money taken from those killed, collecting cash in different currencies from across Europe.
He also performed "ramp duty", guarding the luggage stolen from deportees as they arrived by rail at the extermination and forced labour camp in Nazi-occupied Poland, they said.
Gröning has not entered a plea, since under the German judicial system this is only done once all witnesses have been heard.
'System of mass murder'
The bespectacled Gröning -- who entered court using a Zimmer frame walking aid, wearing a white dress shirt and beige sleeveless jumper -- admitted to performing those tasks.
He spoke for over an hour, declining an offer to take a break.
Many of the more than 100 co-plaintiffs, witnesses, lawyers and reporters listened to him via simultaneous translations in English, Hebrew and Hungarian.
Romanian-born Auschwitz survivor and co-plaintiff Eva Kor, 81, said before the trial that "he is a murderer because he was part of the system of mass murder".
After Gröning's testimony, she expressed appreciation for his attempt to shine a light on his dark past.
"He's very old, and meeting him face-to-face makes me realise that he did the best that he can do with his mind and his body, because he has a lot of difficulties physically and, I'm sure, emotionally," she told reporters outside the court.
"He has to remember a lot of things he did, so I think he is really doing his best."
Gröning, unlike most former Nazis, has spoken at length in a string of media interviews about what he did and saw at Auschwitz, although he has insisted he was not personally guilty of harming any inmates.
Prosecutors say that by serving at the camp, he played a role in the mass murder that claimed over a million lives. They are building their case around the “Hungarian action” in which 450,000 Jews were transported from Hungary to Auschwitz in an eight week period between May and July 1944. 300,000 of them were murdered within this period.
'I saw everything'
Gröning first opened up about his past in 1985, when a member of his stamp collectors' club handed him a book written by a Holocaust denier.
He returned it with the message "I saw everything. The gas chambers, the cremations, the selection process... I was there."
He went on to write a memoir for his family, shared his recollections with the German press and appeared in a BBC documentary.
During the war, Gröning has said, he saw the mass extermination as "a tool of waging war. A war with advanced methods."
He has recounted acts of barbarism he witnessed, including when an SS guard on the railway ramp killed a baby.
"The crying had bothered him," Gröning recalled. "He smashed the baby's head against the iron side of a truck until it was silent."
He recounted the incident again in court on Tuesday.
Gröning had previously been cleared by German courts, but the legal basis for prosecuting ex-Nazis changed in 2011 with the trial of former death camp guard John Demjanjuk.
While previously courts had punished defendants for individual atrocities, Demjanjuk, a former Ukrainian citizen and later Ohio auto worker, was convicted solely on the basis of having served at a camp, Sobibor, also in occupied Poland.
Christoph Hübner, vice president of the International Auschwitz Committee, representing survivors, said the new trial was important because "many perpetrators never saw the inside of a courtroom and died without having been confronted with their guilt."
"This is an enduring scandal that has caused great indignation among the survivors."
Some 1.1 million people, most of them European Jews, perished between 1940 and 1945 in the Auschwitz-Birkenau camp before it was liberated by Soviet forces.
Court dates for the trial have been scheduled until July 27th.