Deputy police spokesman Kwacijwok Dominic Amondoc said the death toll had risen to 13 after some of those who were injured in the shootingduring the screening of an English Premier League match on Saturday night died of their wounds.
Amondoc said 10 others were still being treated in hospital.
Among the injured was Wani Patrick, recovering from a bullet wound to his hand. "When I was shot I fell down and some youths fell on me. I was unable to stand up until he finished shooting all his bullets," he said. "Many people were shot, many people died."
The gunman, who appeared drunk, grew angry after being refused free entry to the bar where patrons had paid roughly $0.50 (0.45 euro cents) each to watch the Chelsea vs. Everton match on television.
The man stormed off, "but when he came back he was carrying a gun and just started shooting randomly," said Amondoc.
The incident happened at around 9:00 pm (1800 GMT) in Gure, a poor suburb in Juba's southwest.
The whereabouts of the shooter are unclear with "investigations underway", according to deputy government spokesman Paul Akol Kordit.
"It's very unfortunate and we as a government condemn this in the very strongest terms possible," said Kordit.