Izzat Abdulhadi will ask Foreign Minister Penny Wong to reinstate the funding to the United Nations Relief and Works Agency for Palestinian Refugees (UNRWA).
"It's very disappointing and it will impact a lot of lives in the Gaza Strip," he told AAP.
"It increases starvation, it will increase the suffering of the Palestinian people in Gaza - it's a double standard from the international community.
"It's the collective punishment of 5.6 million Palestinian refugees."
That 12 people are being investigated within an agency of 30,000 people shouldn't mean vital aid is paused to millions of people, Mr Abdulhadi said.
"This is urgent, this is significant and very important," he said.
"Naturally this position will increase anger and radicalisation within the Arab Muslim community within Australia.
"It's a UN organisation, it has a lot of scrutiny and budget monitoring, it's propaganda to liquidate the UNRWA."
The UN was taking swift action following the "extremely serious allegations", Secretary-General Antonio Guterres said.
Allegations UNRWA staff were involved in the abhorrent October 7 terror attacks are deeply concerning. — Senator Penny Wong (@SenatorWong) Australia welcomes UNRWA's swift response and will engage closely on investigations.We are speaking with partners and will temporarily pause disbursement of recent funding. pic.twitter.com/Havwserjh3January 27, 2024
Australia's decision has also been slammed by the Australian Palestine Advocacy Network, saying it went against Australia's obligation to prevent genocide in Gaza.
The International Court of Justice (ICJ) delivered an interim ruling that Israel needed to take measures to prevent genocide but didn't order a ceasefire in the besieged enclave.
Israel has been limiting food, supplies and aid into Gaza, with the United Nations warning of mass starvation.
It was hypocritical of the Australian government to issue a statement of support for the ICJ ruling while immediately halting "life-saving funding" following the allegations about the UNRWA, the Palestinian network said.
It urged the government to "immediately change course and to begin to act with legal and moral consistency to put an end to Israel's killing, maiming, starvation and collective punishment of Palestinians in Gaza".
New Zealand hasn't immediately frozen aid, with its foreign affairs ministry saying it had confidence in the UN to investigate and it expected "findings will be met with an appropriate response".
It would re-assess the situation again before releasing its next round of funding for the agency in 2024, the ministry said.
But Australian Liberal frontbencher James Paterson expressed little faith in the agency's ability to investigate after allegations Hamas had been siphoning money.
"Inadequate responses to allegations like that in the past mean that we cannot have confidence that this investigation that they've announced will be sufficient," Senator Paterson told ABC radio.
While Australia has a role to play in providing humanitarian aid, "we have to be absolutely rigorous in ensuring that Australian taxpayer dollars doesn't end up funding a terrorist organisation," he said, supporting the government's decision.
Hamas is designated a terrorist organisation by the Australian government.
Other aid groups such as the Red Cross or Red Crescent could be used to support Gazans, the senator added.
But Mr Abdulhadi said the UNRWA was the main service and couldn't be replaced by any organisation.
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