A push to block ISIS fighters from returning home has “got nothing to do with One Nation” despite Pauline Hanson’s offer to help change laws, according to the Coalition.

The One Nation leader wrote to Opposition Leader Angus Taylor on Thursday night, pledging support for legislation intended to strengthen Australia’s counter-terrorism laws.

Deputy Liberal leader Jane Hume on Friday said the Coalition needs Labor’s votes to pass its legislation, not One Nation’s.

It comes as 13 Australian men, including a Perth-born doctor nicknamed “Dr Jihad,” are being held in an Iraqi prison while seeking a possible return to Australia.

Appearing alongside Health Minister Mark Butler on Channel Seven’s Sunrise, Ms Hume said the Coalition had “led the fight against bringing these ISIS sympathisers home”.

“But we didn’t just talk about it, we actually did the work, we prepared the legislation, and we introduced it into Parliament – we did that back in March,” she said.

“The problem here of course is that it’s not One Nation’s votes that we need to pass this legislation, and Pauline should know that after 30 years in politics.

“We simply don’t have the numbers even with One Nation. It’s Labor’s votes that we need to make sure that we can shut the door on ISIS terrorists, sympathisers, coming back to our shores.”

Addressing Mr Butler, Ms Hume then said: “It’s up to Mark to tell us why we can’t get this done because the legislation is there”.

“We don’t need One Nation, we need Labor. Otherwise, we simply don’t have the numbers.”

Questioned about the legislation push, Mr Butler claimed the Albanese government “don’t know what the proposed laws are” that One Nation wants to endorse.

“I suspect this one of many sucker balls that are going to be bowled at Angus Taylor by Pauline Hanson between now and the next election,” he said.

“Jane’s right, the current laws were put in place by the Coalition during their last term in government. With our support as the opposition, they were considered very carefully by the bipartisan committee on intelligence and security.”

It comes after Ms Hanson penned a letter to Mr Taylor, expressing her party’s commitment to supporting legislation that aims to keep individuals associated with terrorist groups out of Australia.

She stated that One Nation would collaborate with the Coalition on any legislation intended to strengthen Australia’s counter-terrorism laws.

“One Nation will vote with the Coalition, in both chambers, for legislation that strengthens Australia’s counter-terrorism laws to the fullest extent permitted by the Constitution, including the laws governing temporary exclusion, terrorism offences, bail, citizenship consequences, passport issuance powers and post-release supervision,” her letter reads.

“We will support every lawful measure necessary to protect Australians from those who voluntarily joined terrorist organisations overseas.

“The Coalition wrote the current laws and knows exactly where they now need strengthening.

“Let’s work together to draft these bills. We will back them. I do not care whose name is on the paper.

“I care that it passes before the gates of that Baghdad prison open.”