The man, whose face is not clear under a dark baseball cap, can be seen entering the building, taking a Kalashnikov automatic rifle from a bag and opening fire through a door on his victims -- an Israeli couple, a French woman and a young Belgian man.
Police described the man as of medium height and athletic build. He carried out the attack deliberately and unhurriedly, leaving the scene on foot.
The Israelis and the French woman, who worked as a volunteer, died on the spot. The young Belgian died of his wounds today.
Police said earlier they had been unable to identify the gunman so far and released the video footage as they called for witnesses to come forward.
Officials say they have not established any motive for killings, and no group has claimed responsibility, but the Jewish community and many others see it as an anti-Semitic attack.