Grace Tame has hit back at Pauline Hanson after the One Nation leader called for Australia’s domestic intelligence agency ASIO to investigate the former Australian of the Year over her involvement in a pro-Palestine rally in Sydney.

Ms Tame drew criticism after leading crowds in chanting “globalise the intifada” during a mass demonstration opposing Israeli President Isaac Herzog’s state visit to Australia on Monday. The chant, which has become common at pro-Palestine protests internationally, is widely regarded as anti-Semitic because of its association with violence against Israelis. It has been banned in Queensland, with a similar prohibition under consideration in NSW.

Writing on social media on Tuesday, Senator Hanson said Ms Tame’s actions should raise alarm bells for authorities.

“Grace Tame’s support of a global intifada should be a terrifying trigger for ASIO and other police agencies to investigate who she’s hanging out with,” Senator Hanson wrote.

Ms Tame responded shortly afterwards with a sarcastic post, saying: “I can tell you now Pauline, I hang out with a bunch of neurospicy sexy queers and culty cyclists.”

The controversy intensified after fellow One Nation figure Barnaby Joyce argued Ms Tame should be stripped of her Australian of the Year title, which she received for her advocacy on behalf of survivors of sexual assault.

At the rally, Ms Tame urged protesters to continue mobilising against Israel’s actions, leading the chant: “From Gadigal to Gaza, globalise the intifada.”

Speaking to Sky News on Tuesday, Mr Joyce said Ms Tame had failed to live up to the responsibilities that come with a national honour. “You have a responsibility when given an honour by the Australian people to basically conduct yourself in a way that inspires the harmonious nature of Australia,” he said.

“We are not … softies, but we have an egalitarianism, a robustness, we have a cheek about us, but we do not inspire this sort of division, this hate.”

Mr Joyce claimed the slogan carried deadly implications. “The form of her words, if it’s followed through, brings about the death of people,” he said. “People will be, on the premise of their religion, of their race, they will be murdered.”

Intifada is an Arabic word meaning “uprising”, but it is closely linked to two periods of sustained violence in the Israeli-Palestinian conflict.

The First Intifada, from 1987 to 1990, involved widespread Palestinian protests and violent attacks on Israelis. The Second Intifada, from 2000 to 2005, was far deadlier, with about 1000 Israelis killed in shootings and suicide bombings. Thousands of Palestinians were also killed in Israeli military responses.

Senior Labor figures have also distanced themselves from the chant. Cabinet minister Tanya Plibersek said its use ran counter to Australia’s long-standing support for a two-state solution.

“What it means is a single state – a single Palestinian state or a single Israeli state,” Ms Plibersek told reporters at Parliament House. “That is a damaging and divisive message.”

Ms Plibersek said Labor backed a negotiated settlement that allowed Israelis and Palestinians to live securely side by side.

“We don’t support slogans or chants or statements that suggest a single state because a single state means pushing the other people out,” she said.

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