Claims that halal certification funds terrorism “don’t check out”, and significant flaws in the argument haven’t been answered, an investigation by the ABC shows.

The claims were aired in national Reclaim Australia rallies that also protested against any introduction of sharia law in Australia – which is not being proposed.

The ABC Fact Check investigation showed that a central element of the anti-halal campaign, that it “spins an estimated $3 trillion a year”, was not possible.

The claim has been made by blogger Kirralie Smith and repeated by One Nation leader Pauline Hanson.

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“It’s estimated it’s a $3 trillion industry and this money can go to mosques, Islamic schools and it’s even estimated that it can go to terrorism,” Ms Hanson said while campaigning in the Queensland election, the ABC reported.

When asked to show evidence for the claim, a One Nation spokeswoman pointed to “plenty of articles written and shows aired”.

Citing Malaysian research from 2012, Fact Check showed that worldwide the halal food industry was worth between US$600 billion and US$2.1 trillion. In other US statistics global Muslim food and drink spending added up to $1.3 trillion.

“None of these figures reach $3 trillion,” Fact Check states.

“In any case, all the estimates are for the value of halal food, not the value of certifying that food.”

The authors also looked for evidence to suggest a link to terrorism from halal certification, and couldn’t find any.

Fact check said the Australian Federal Police and the Australian Transaction Reports and Analysis Centre (Austrac) stated they had “no information to indicate there are links to terrorism financing from halal certification fees”.

The agencies monitor and police money laundering and terrorism.

The report found that money paid for halal certification, which was estimated by some food producers at between 0.003 per cent and two per cent of contract totals, went to schools, mosques and other Islamic organisations.

“While the proceeds of halal certification do fund Islamic organisations, Fact Check could find no evidence that this money has ever flowed to terrorist groups.”