Capital punishment should be reinstated as a punishment for people who commit acts of terrorism on Australian soil, the Coalition backbencher George Christensen has argued.

The MP reiterated an earlier call to bring back state-sponsored execution during a speech on Tuesday on the government’s bill to strip dual nationals of their Australian citizenship if convicted of terrorism offences.

Extremists who kill Australians in acts of terrorism should be put to death, he told the House of Representatives.

“It’s something that seriously needs to be considered,” he told the chamber, shortly after the prime minister, Malcolm Turnbull, made a speech on Australia’s national security response to terrorism.

“There is no question that we are at war with radical Islam,” Christensen said. “Under these circumstances, it’s appropriate that we take whatever steps are necessary to protect Australians, to protect our citizens.”

Christensen supports the bill to strip dual nationals of their Australian citizenship but wants it to go even further and apply to sole nationals, too.

“What do you do with people who don’t have a second country option?” he asked. “My view is still to strip them of citizenship – they should forfeit all rights of citizenship.”

Borrowing heavily from the sentiments of the former prime minister Tony Abbott, Christensen argued that sole nationals who have committed acts of terrorism should have their citizenship “downgraded” to reduce their rights to work, welfare and movement in and out of the country.

“When Australians are fighting against their own country and the values it stands for, they have signed their own ticket out of this country,” the Queensland Liberal National MP said. “Like any other club, when you break the rules, you forfeit your membership. If you decide you no longer want to adhere to the rules, you hand your membership in.”

He wants those who advocate for sharia, which he labelled the “antithesis of Australian society”, to also be stripped of their citizenship. Supporting sharia means “you are writing your ticket out of this country yourself”, he said.

The comments come days after the independent senator for Tasmania, Jacqui Lambie, called for new citizens to pledge alliance to Australian law rather than sharia.

“We do have the right and duty to discriminate on the basis of whether prospective citizens will accept and uphold our democracy and culture, our Australian laws,” she said last week. “Therefore, a key test of whether people are worthy of our compassion and are suitable for citizenship is their opposition to sharia – or terrorist law, as we call it.”