The national security committee of cabinet was briefed about all aspects of the American refugee swap deal in late 2016, including the resettlement of two Rwandan men accused of murdering tourists in Uganda.

Guardian Australian understands the NSC was briefed, and the then treasurer, Scott Morrison, the home affairs minister, Peter Dutton, and the foreign affairs minister, Julie Bishop, were aware of all the elements of the agreement signed by Malcolm Turnbull and Barack Obama in 2016.

The advice from the US was the two men did not pose a security risk to Australians.

On Friday Morrison told reporters the two men, former members of a Hutu rebel army implicated in the Rwandan genocide, were assessed and accepted by Australian authorities between April and July last year – during Turnbull’s period as prime minister.

“In these cases … these specific allegations were reviewed by our security agencies and by our immigration authorities, and they were not found to be upheld in their view, and as a result they were allowed to come to Australia,” the prime minister told reporters in Queensland.

“That process went through between about April and July of last year, when that process was pursued.”

Morrison’s comments about the timeline appear to be an attempt to distance the controversy from his leadership, which began in August after the spill against Turnbull.

Morrison refused to comment on the fact that family members of victims and survivors of the Uganda attack were not told the two accused men were in Australia.

“These are very sensitive matters, when you’re dealing with any refugee cases,” he said. “And the privacy of those arrangements is always important. Whether you’re dealing with Sri Lankan refugees, whether you’re dealing with Iraqi refugees, Syrian refugees, indeed, or those out of the Sudan.

“And we always respect the privacy, and the privacy of the process, for those individuals, because when you’re providing refugee protection, then that is an important part of the process and an important obligation.”

Politico reported on Thursday the men had arrived in Australia in November, linking their case to the refugee deal between the Australian government and the Obama administration.

In 2017 a leaked transcript of a phone call between Turnbull and newly elected US president, Donald Trump, revealed the Australian leader apparently seeking to reassure Trump, who labelled the arrangement the “worst deal ever”.

Turnbull said Australia would be taking people the Obama administration “were very keen on getting out of the United States”.

“We will take more. We will take anyone that you want us to take,” Turnbull said.

Leonidas Bimenyimana and Gregoire Nyaminani, as well as a third Rwandan man, had confessed to their involvement in the 1999 murder of eight tourists – four Britons, two Americans and two New Zealanders – on a gorilla-watching trip in the Ugandan rainforests. The trio were sent to the US to face trial for the murder of the two US victims, with prosecutors seeking the death penalty.

However, a district court judge dismissed the case in 2006, finding that the men’s confessions were the only evidence against them and had been obtained through torture.

The men then claimed they could not be returned to Rwanda because they would be persecuted, and they remained incarcerated and in limbo in the US until Bimenyimana and Nyaminani were sent to Australia.

Ahead of Saturday’s federal election, Morrison has been forced to provide increasing detail of the government’s decision to accept the two men, after originally refusing to comment on specifics.

On Thursday evening he confirmed the men were in Australia but said they had been screened by security agencies.

“That included checks relating to national security, criminality, war crimes, and crimes against humanity,” he said.

“That resulted in an assessment that they did not represent a risk to security and they were cleared.”

The government’s acceptance of two men linked to a brutal mass murder and rebel groups implicated in a genocide has drawn criticism in light of the government’s opposition to laws allowing for the medical evacuation of sick refugees and asylum seekers on Nauru and Manus Island.

The government had insisted passing the bill would mean criminals, including accused murderers, could be brought to Australia.

“It doesn’t provide for the usual arrangements which would enable us to reject someone coming to Australia because they have a criminal history,” Morrison said in February.

“They may be a paedophile, they may be a rapist, they may be a murderer and this bill would mean that we would just have to take them.”