There is “no immunity” for members of the country’s armed forces.
He told a weekly cabinet meeting that the soldiers involved would be punished, and rejected international pressure over the issue ahead of a visit to Jakarta by Australian Prime Minister Julia Gillard.
“It became a news topic in various international media and we must take steps. Not because of pressure from anyone,” he said.
“That (torture) is not this country’s policy. If there’s a violation, we will pass sanctions. There’s no immunity.”
Military chief Agus Suhartono said five suspects had been identified and their files had been passed to military prosecutors. He did not name the suspects.
The video, which appeared online, showed two Papuan men being kicked and abused as soldiers interrogated them over the whereabouts of a weapons cache. One screams in pain when a burning stick is applied to his genitals.
The video, first reported in the Sydney Morning Herald newspaper, follows similar allegations against Australian-funded Indonesian anti-terror police said to have abused peaceful political activists in the Maluku islands.
Papua and the Malukus have underground separatist movements which Indonesia regards as threats to its territorial unity. Activists are regularly given lengthy jail terms for crimes such as possessing outlawed rebel flags.
New York-based Human Rights Watch (HRW) has urged Gillard to press Indonesia for a full investigation into torture by its military during her talks with Yudhoyono in Jakarta on Tuesday.
Yudhoyono said however that Indonesia needed no outside pressure to “do what needs to be done”.
“I read in the news… Australia has been asked to pressure Indonesia to carry out an investigation. I say there’s no need to pressure Indonesia,” said.
“There should be no pressure from any country or any non-government organisation.”
Australia has worked closely with the Indonesian security forces since 88 Australian tourists were killed in the 2002 Bali bombings by Islamist extremists.
Few Indonesian military officers have ever faced justice for gross human rights abuses dating back decades, including alleged crimes against humanity in East Timor.