Indonesia's government called on police Monday to identify and punish those responsible for a stadium stampede that left 125 people dead, as anger mounted over one of the deadliest disasters in the history of football.

The tragedy on Saturday night in the city of Malang also saw 323 people injured after officers fired tear gas in a packed stadium to quell a pitch invasion, triggering a stampede.

"We ask the national police to find the perpetrators who have committed crimes in the next few days," Indonesia's chief security minister Mahfud MD said in a broadcast statement.

"We asked them to unveil who has perpetrated the crimes and take action against them and we also hope the national police will evaluate their security procedures."

He announced that a task force had been formed for an investigation.

The incident unfolded when fans of home team Arema FC stormed the pitch at the Kanjuruhan stadium after their loss 3-2 to bitter rivals Persebaya Surabaya.

Police responded by launching tear gas into packed terraces, prompting spectators to rush en masse to small gates where many were trampled or suffocated, according to witnesses.

Police described the incident as a riot and said two officers were killed but survivors accuse them of overreacting and causing the deaths of scores of spectators, including a five-year-old boy.

"One of our messages is for the authorities to investigate this thoroughly. And we want accountability. Who is to blame?" said 25-year-old Andika, who declined to give his last name.

"We want justice for our fallen supporters."

National police spokesman Dedi Prasetyo said investigators were analysing CCTV footage around the stadium to identify "suspects who have perpetrated the destruction".

They also planned to question event officials on Monday as well as 18 officers responsible for being "the carrier or the operator of the weapons", he told a televised press conference.

- 'Murderer' -

In a tearful live address, Arema FC president Gilang Widya Pramana apologised for the club's role in the tragedy.

"I, as the president of Arema FC, will take full responsibility for the incident that occurred. I deeply apologise to the victims, their families, all Indonesians, and Liga 1."

Newspaper Kompas published a black front page with the word "tragedy" and a stadium bearing the names of victims.

Outside the Kanjuruhan venue on Sunday evening, people held a vigil to honour the victims beneath a roaring lion statue that is the club's symbol.

Graffiti daubed on the walls revealed bubbling anger towards authorities.

"My siblings were killed. Investigate thoroughly," read one message scrawled on the stadium's shutters, accompanied by a black ribbon and the date of the disaster.

"ACAB", an acronym for "all cops are bastards", was sprayed on another wall.

In Jakarta, hundreds of football fans gathered outside the country's biggest stadium on Sunday chanting "murderer, murderer".

Indonesian President Joko Widodo announced a probe, but rights groups said it should be independent and officers should be held accountable for using tear gas in a confined area.

"We call on authorities to conduct a swift, thorough and independent investigation into the use of tear gas at the stadium and ensure that those who are found to have committed violations are tried in open court," Amnesty International said in a statement.

"This loss of life cannot go unanswered."

Mahfud said the task force for the investigation would consist of government officials, analysts, ministry representatives, football officials, academics and members of the media.

"It is estimated the task can be concluded in the next two or three weeks," he said.

- 'Died in the arms of players' -

Anger against authorities gathered pace online, with many critical posts going viral.

"Investigate thoroughly. Firing tear gas in a closed space full of humans is a serious violation," read one tweet that was liked 11,000 times.

An online petition titled "The police must stop using tear gas" had gathered nearly 6,000 signatures by Monday morning.

More information emerged about the horrors of the stampede, with Arema FC's Chilean football coach saying "fans died in the arms of players".

"I think the police overstepped the mark," Javier Roca told Spanish broadcaster Cadena Ser.

Fan violence is an enduring problem in Indonesia.

Witnesses of Saturday's episode say supporters of the home team invaded the pitch after their loss to Persebaya Surabaya.

Persebaya Surabaya fans had not been allowed to buy tickets to the game, due to the fear of violence.

After the stampede, Arema fans threw rocks at officers and torched vehicles including a police truck on the streets of Malang, according to police.

FIFA's president Gianni Infantino called the tragedy a "dark day" for football.

The world governing body's safety guidelines prohibit the use of crowd control gas by police or stewards at pitchside.