Vitaly Kaloyev, 48, lost his family when a DHL cargo plane and a Russian passenger jet collided in Swiss-controlled airspace over southern Germany on July 1, 2002.
He is charged with the premeditated killing of Peter Nielsen, the only air traffic controller on duty at the time.
Under Swiss law this charge ranks between murder and manslaughter and carries a maximum sentence of 20 years.
"I went to Nielsen as a father who loves his children, so he could see the photos of my dead children and next to them his kids, who were alive," Kaloyev told a packed courtroom.
"Everyone can make mistakes, but these are my children," the trained architect and construction engineer said.
Looking gaunt but clean-shaven, Kaloyev spoke in Russian and in a monotone voice, telling the prosecutor that since the deaths of his children, aged 10 and 4, he had lost the will to live.
When the judge asked what Kaloyev intended to do whenever he left prison, the Russian replied: "I don't know how to live."
The Russian allegedly paid a detective to find out Nielsen's address and confronted him on the terrace of his home near Zurich airport on February 24, 2004, stabbing the Dane to death in front of his wife and three children.
He has made a partial confession already but argues the stabbing was not premeditated. He has been held in Swiss jail since shortly after the crime. A verdict is expected on Wednesday.
Kaloyev, from North Ossetia, was working in Spain at the time of the crash.
The mid-air collision over the German village of Ueberlingen, close to the Swiss border, killed 69 people, mostly children, travelling on a Bashkirian Airlines flight from Moscow to Barcelona. Two DHL pilots also died.
Nielsen, 36 when he died, had been alerted to the intersecting flight paths just 44 seconds before the two aircraft collided.