Malcolm Turnbull has flagged strengthening Australia’s counter terrorism regime following the coronial report into the Lindt Cafe siege.

The prime minister told parliament on Wednesday the federal government would consider the recommendations of the Sydney siege inquiry “carefully” and continue to “strengthen arrangements where needed”.

“We must be more agile than those who seek to do us harm,” Turnbull said. “Our agencies, with whom I and my ministers are in constant touch, are constantly upgrading, reviewing, adjusting our response measures.”

While Turnbull gave a general signal about strengthening the national regime, the man who was prime minister at the time of the incident, Tony Abbott, went further. Abbott used a radio interview to argue police needed to be handed shoot to kill powers during terrorist events, and the military needed to be much more hands on.

“We need to change our protocols dealing with terrorist sieges because terrorists don’t expect to get out alive and they don’t care who they kill,” Abbott told 2GB.

“I think we do need to give the police a shoot to kill power when they reasonably think they are in a terrorist situation, and we do need to ensure, without supplanting the appropriate role of the police as the lead agency in a terrorist situation, that there is close cooperation, without muddying the lines of command, close cooperation between the military and the police,” he said.

Abbott declared that the Lindt cafe gunman, Man Haron Monis, had been given the “kid glove” treatment. “The other thing is to note that [at] every stage this evil murderer was given the kid glove treatment, even it seems in some ways on the day of the siege and he was given the benefit of the doubt all the way through.”

He said Australia needed a multi-pronged approach to reduce the threat of terrorism, including positive relationships with people he termed “live and let live Muslims”.

“We need the strongest possible attack on terrorist sanctuaries in the Middle East, the best possible security agencies and police forces here at home, and we need to work with ‘live and let live Muslims’ to end the death to the infidel mindset which is the root cause of this kind of terrorism.”

The NSW report noted that police had underestimated the threat the gunman posed, there was confusion around the lines of command during the incident, and the police response – “contain and negotiate” – failed.

The report said special powers available to police responding to terror incidents should include more clearly defined rights to use force, and impediments in information sharing between state and federal authorities should be removed.

It noted the defence forces can only intervene in incidents if the federal government believes the state police force can not mount an adequate response.

In Senate estimates, the attorney general George Brandis also faced sustained questioning from Labor over his handling of correspondence from the gunman.

Man Haron Monis wrote to Brandis in October 2014, two months before the Lindt cafe siege. The correspondence was not passed on to the inquiry.

Brandis told the Senate the government had implemented changes to ensure letters such as the one written by Monis will be passed on to the Australian Security and Intelligence Organisation.

The coroner’s report noted there was no effective policy in place to require the commonwealth bureaucracy to forward correspondence received by it to Asio where that correspondence relates to security considerations.