The federal attorney general, George Brandis, has warned against alienating Australian Muslims, saying this would be the “worst thing we could do” in response to the terrorist attacks in Paris.

Senior government ministers have sought to reinforce Malcolm Turnbull’s message that the Muslim community is a crucial partner in the fight against Islamic State and that security agencies are doing everything they can to keep people safe.

But in the wake of Friday’s deadly attacks in the French capital, the prime minister is facing an internal push to appoint the immigration and border protection minister, Peter Dutton, as a permanent member of the cabinet’s national security committee.

The calls are backed by the former prime minister, Tony Abbott, who said Dutton’s ministry was “a significant part of our national security machinery”.

Abbott also used an interview with 2GB on Monday to call for “a movement inside Islam that makes it absolutely crystal clear that anything that smacks of ‘death to the infidel’ is wrong and it should have no place in anything that claims to be of God”.

Australia’s terrorism alert level has remained at “high”, the second-most serious level, since last year when the government began a series of legislative changes to expand the powers of security agencies and committed to airstrikes against Isis in Iraq.

Brandis said there was “no evidence of a connection between the events in Paris and anything bearing upon the security situation in Australia, but of course the government and particularly the national security agencies keep the situation in Australia under constant review”.

“Australia is the most successful multicultural society in the world and the Muslim community are a very important element of Australian society,” Brandis told the ABC on Monday.

“The fact that a very small minority of fanatics defy the teachings of the Islamic religion by engaging in terrorist crime, whether overseas or, as we have seen on three instances now in the last year, in Australia, should not reflect upon the Muslim community. The worst thing we could do is to alienate the Muslim community. They are our fellow citizens and they are our necessary partners in combating this menace.”

Brandis was responding to a question about a call from the deputy Speaker of the NSW lower house, Andrew Fraser, to close the borders.

Fraser, a Nationals state MP, wrote on Facebook on Saturday: “Message to Malcolm Turnbull : Australia does not need Middle Eastern refugees or Islamic boat people! Close our borders we have enough anarchists already resident in Australia,( our democracy),we do not need any more coming in disguised as refugees!!!!!!”

Fraser, whose daughter lives in France, told Guardian Australia he wanted a “far better filter” on the refugees coming to Australia and denied he was tarnishing all Muslims.

“I’m not saying all Muslims are terrorists but I’m saying the majority of terrorists are Muslims,” he said.

Asked about Brandis’s comments about the importance of not alienating Muslims, Fraser said: “I don’t disagree but we’ve got to make sure that we don’t have Islamic terrorists enter Australia under the guise of refugees.”

Dutton did not signal any changes to the government’s plan to accept 12,000 Syrian refugees, but said the “prudent” security checks would not be rushed.

“We are talking about people who are fleeing from the Assad regime or fleeing from Isis themselves,” he told 2UE on Monday.

“They are people, Christians for example, who were living in villages that have been attacked by Isis, they’ve had family members lost to terrorist attacks themselves, so they’re the people that we’re targeting under this scheme. We are not going to compromise on the security checks.”

Dutton implied that the prime minister might soon consider changes to his status on cabinet’s national security committee, pointing to Turnbull’s statement in September that the arrangements would be monitored.

“The PM made it clear that it was under review and I think that’s perfectly reasonable, so no doubt he’ll consider that in the coming days and weeks,” Dutton said.

Dutton is no longer a permanent member of the committee but is “co-opted” to attend when necessary. He confirmed he had attended at least one meeting since Turnbull became prime minister, to give an update on Operation Sovereign Borders.

Dutton cautiously endorsed comments made by the Tasmanian Liberal MP Andrew Nikolic in the Australian newspaper for the immigration and border protection minister’s status to be upgraded to permanent membership.

“[Nikolic is] obviously one of our finest in parliament, having served our country for 30 years in the army,” Dutton said. “The point he makes is border security is very important to our national security – and the prime minister obviously recognises that; of course he does.”

Abbott said it was up to the prime minister to decide on cabinet committee memberships, but added: “The minister for border protection is, in my judgment, a significant part of our national security machinery.”

Abbott’s interview with broadcaster Alan Jones on Monday also canvassed the broader threat of terrorism. The former prime minister said he hoped “this latest atrocity in Paris” and other recent attacks “makes us more determined than ever to protect our way of life, to stand up for our values”.

“Thank God the Australian government under my leadership and subsequently has put strong border protection policies in place, we have put strong national security policies in place and we are playing a significant part in the international campaign to disrupt and destroy this death cult, this Islamic State caliphate,” Abbott said.

“The problem that we’ve got with all of these terrorist attacks is that the people carrying them out are claiming to have done it in the name of Islam. The overwhelming majority of Islamic people around the world, I am sure, find this utterly, completely, absolutely abhorrent but there is a problem when these evil atrocities are done in the name of a particular religion.”

Turnbull has indicated Australian peacekeepers could play a role if there was a political settlement in Syria, but the defence minister, Marise Payne, said such a step was “some way off”.

Payne told the ABC the defeat of Isis in Iraq and Syria remained “of primary importance” and any change to Australia’s military involvement would “be a considered step”. She suggested the government would consider the situation on Turnbull’s return from overseas.

The treasurer, Scott Morrison, urged people to get on with their lives and stand strong in the face of terrorism.

“What they want us to do is to be struck down in terror and horror,” he told 2GB.

“The best thing Australians can do, apart from expressing their great sympathies and prayers for those who have been affected, is to get about their day, to go about their lives, to prepare for Christmas, to spend time with friends and family, to rejoice in the wonderful country in which we live and send the best possible message that that ain’t going to change.”

The Labor leader, Bill Shorten, said people must not “fall into the trap of increasing suspicion and fear of each other in this country”. Shorten said Australia should not stop being an immigrant nation.

“If we do that, then the evil people win,” he said.