The Abbott and Baird governments have announced an urgent review into the Martin Place Lindt cafe siege, including an investigation of how gunman Man Haron Monis slipped through state and federal security and legal nets.

The review will look at the arrival in Australia of Monis, an Iranian, and the decision to grant him of asylum, permanent residency and citizenship, as well as the social security support he received.

Also under scrutiny will be:

• information held by Commonwealth and NSW agencies about Monis before and after his arrival, up until this week’s siege;

• how any information relevant to public safety was shared between agencies;

• Monis’s interaction with the NSW justice system – he was out on bail after being charged with being an accessory to his ex-wife’s brutal murder – and his access to firearms;

• whether national security powers, including control orders, were used, or could have been used, in relation to his activities of security concern;

• any lessons learned by NSW and federal police about the handling of the siege;

• the effectiveness of public communication, including the co-ordination of messaging between the Commonwealth and NSW; and

• the effectiveness of general federal-state co-ordination.

Two hostages as well as Monis were killed in a firefight in the early hours of Tuesday morning, and several people were injured.

Monis initially took 17 hostages on Monday morning at the popular cafe. Some later escaped, the last of them just before the firefight. Exactly what happened during the firefight remains unclear.

There are also investigations underway by the NSW Coroner and state and federal police.

The federal-state review is to be handled by the newly arrived secretary of the Prime Minister’s department, Michael Thawley, and the secretary of the NSW Premier’s Department, Blair Comley (who took up his state position after being sacked by the Abbott government). It will report by the end of January.

At a news conference on Tuesday, Prime Minister Tony Abbott said he had “great confidence” in the police and security agencies but “nevertheless, we do need to reflect on what’s happened and to ponder what might have been done better.”

We needed to know why the perpetrator of this “horrible outrage” had got permanent residency, how he could have been on welfare for so many years when he appeared to be able-bodied if not necessarily of sound mind, and what he was doing with a gun licence.

“I share the exasperation of the Australian public at what appears to be someone who has been having a lend of us” for so many years, Abbott said.

“We particularly need to know how someone with such a long record of violence, such a long record of mental instability was on bail after his involvement in a particularly horrific crime.

“And we do need to know why he seems to have fallen off our security agencies' watchlist, back in about 2009.”

Asked whether his confidence in the security and police agencies would be shaken if it were shown one of the hostages had been shot by the police, Abbott said the police inquiry would be looking at what happened inside the cafe.

“When you are in a firefight all sorts of things happen. I’m not going to go into operational details. But the important thing for the police in the situation like that is to take care of the terrorists as quickly as possible.”

Abbott said there was “incredulity” around the national security committee of cabinet, from both ministers and officials, on Tuesday when it was briefed on the details of Monis' record and his life in Australia.

He said NSW Premier Mike Baird was confident that if had Monis' bail application been made under the new rules the Premier has put in place, it would not have been granted.

Abbott said his instruction to agencies was that anyone thought to be a potential terrorist “needs to be monitored as carefully and as closely as we can.” Each agency, in the light of what had happened, was asking itself how it could do better.

The federal-state inquiry’s report will be considered alongside a review of the security machinery of the federal government.

Abbott said he did not know why Monis had fallen off the watchlist around the time he was sending offensive letters to the families of dead soldiers. It was necessary to try to ensure that people only went off the list if they really were no longer a potential threat, “and plainly this individual was”.

Monis had “sought to clothe himself in the symbolism and ideology” of Islamic State but how much contact he had had with it, and what chatrooms or websites he might have been accessing, was not known. “That’s one of the many matters that will be carefully considered in coming days and weeks.”

Abbott said he would not deny or confirm that Iran had tried to extradite Monis at some point.

Abbott said it was important that the security status of people coming from “difficult countries and with difficult backgrounds and claiming asylum” be considered carefully.

Abbott did not want to suggest that people coming to Australia under various humanitarian programs were security risks but any doubts had to be resolved.

Asked whether Monis had been on the FBI’s watch list, Abbott said he could not go into what he might have been to other countries. But he said US President Barack Obama had told him the American security services would be co-operating fully with Australian efforts to get to the bottom of what had happened with Monis.

Michelle Grattan does not work for, consult to, own shares in or receive funding from any company or organisation that would benefit from this article, and has no relevant affiliations.