The Greens and asylum seeker advocates say Mr Berati was "murdered" on the island, but the Government says it will wait for the findings from its official review before commenting on individual reports about what took place.
Immigration Minister Scott Morrison has warned the report, to be conducted by former Attorney-General's Department secretary Robert Cornall, will take "some time" to gather the facts about the "very serious incident" in which 67 asylum seekers were injured.
The review is likely to take months, but the Mr Morrison says it could take longer.
"I have indicated over the next few months I would like to see this matter at least get to some point of knowledge on this," he told reporters in Canberra.
"If that is not possible, it will take longer and [Mr Cornall] will be given support to do that."
Mr Berati arrived at Christmas Island with no family members on July 24 and was transferred to PNG one month later under the resettlement policy introduced by former prime minister Kevin Rudd.
One asylum seeker was flown to Australia for treatment for head injuries as a result of this week's riots. Four others, including one shot in the left buttock, are being treated in Port Moresby, while another asylum seeker is awaiting transfer to the capital.
Mr Morrison says he takes responsibility for things that happen on his watch.
"I do take responsibility for things that happen within my portfolio under my management, of course I do," he said.
"Since we came into office, I have been taking steps every day to try and upgrade and get the offshore processing facilities in a far better shape."
Greens say review not good enough
Mr Cornall has previously looked into sexual assault allegations on Manus for the Labor government, giving him experience in dealing with jurisdictional issues of conducting an investigation in another country.
But Greens leader Christine Milne says the review is not good enough.
"The reality is the last Cornall report was so heavily redacted with so much doubt you only really got the recommendations and that's what's going to happen again," she said.
"And the second thing is there was so many gag orders in place people are not able to speak out.
"I mean what guarantee have we got that the eye witnesses to the murder of Reza Berati are going to be interviewed or their testimony made public so the Australian community can actually come to terms with who actually murdered him and who employed them."
Senator Milne says a royal commission should be ordered.
Asylum seekers 'on the back foot'
Mr Morrison says the Government's offshore processing policy was being tested and he expected further tests.
"There will naturally, and by definition, be a tension in these centres because people don't want to be there in the first place," he said.
The Government's review will "complement" the investigations being carried out by the PNG authorities.
Mr Morrison says his stop-the-boats policy has seen another week go by with no asylum seeker vessels reaching Australia.
He says he believes he has people smugglers "on the back foot".
"Operation Sovereign Borders is stopping the boats, but the boats are not yet stopped," he said.
"We don't take a day off ever when it comes to stopping the boats."
The military commander in charge of Operation Sovereign Borders, Angus Campbell, is on his way back from Manus Island and will brief the Government upon his return.