The president offered "condolences on the death of our compatriots."
PSSI said in a statement earlier that Arema would not host any more games for the rest of the season.
A team had been formed to investigate the incident, PSSI said.
"We regret the action of Arema supporters at Kanjuruhan Stadium," PSSI chief Mochamad Iriawan said.
"We offer condolences and apologize to the victims' families and all parties for the incident," he said.
Afianto, the police chief, said security personnel followed procedures when they fired tear gas after about 3,000 fans invaded the pitch.
"If the fans had followed the rules, this incident would not have happened," he said.
Security personnel are banned from using crowd-control gas and firearms at stadiums under FIFA stadium safety and security regulations.
"The Indonesia Football Association may have been negligent for not informing the police that security procedures at a soccer match is not the same as those at a demonstration," he added.
Witnesses said fans were not attacking rival supporters. Rather, they were demonstrating their disappointment at the players and officials as they left the pitch.
