The Greens have launched an extraordinary attack on new Liberal senator and former military leader Jim Molan, accusing him of overseeing a "humanitarian catastrophe" while directing coalition forces in Iraq.

Key points: Senator Jim Molan headed coalition troops in Iraq during assaults on Fallujah in 2004

Senator Jim Molan headed coalition troops in Iraq during assaults on Fallujah in 2004 Greens say he should bear responsibility for resulting civilian disaster

Greens say he should bear responsibility for resulting civilian disaster Defence Minister, PM and senior Liberals all spring to Senator Molan's defence

Senator Molan had been under fire from Labor and the Greens after sharing anti-Muslim videos posted by the UK far right group Britain First.

But the Greens intensified their criticisms of Senator Molan during Question Time, lambasting his record as chief of operations for coalition forces in Iraq almost 15 years ago.

American, British and Iraqi forces launched multiple assaults on Fallujah in 2004 as they tried to root out Sunni insurgents in the city.

Greens leader Richard Di Natale said the attack on Fallujah was a disaster for civilians, and Senator Molan had to bear responsibility.

"At the time of the assault on Fallujah under the command of now-Senator Molan, a UN special rapporteur said coalition forces used hunger and deprivation as a weapon of war against the civilian population — a flagrant violation of international law," Senator Di Natale said.

"Minister, given Senator Molan's extreme views, do you have a concern these views influenced the decisions he made while executing the military campaign in Fallujah?"

Defence Minister Marise Payne was visibly angered by the question, and was quick to jump to Senator Molan's defence.

"In my 20 years in this chamber I have heard many extraordinary things, but that reflection on the service of a senior Australian army office takes your lows to depths I did not think you could plumb," Senator Payne told the Greens.

"You consistently disappoint the Australian people and you do so with the most extraordinary lack of self-awareness of what it takes to lead your nation in a uniform."

Jim Molan was sworn into the Senate on Monday. ( ABC News: Jed Cooper )

Aid groups say hundreds of Iraqi civilians died during the second battle for Fallujah, although estimates vary wildly.

The US military denied it deliberately withheld food or water from civilians, but conceded supplies were sometimes disrupted by combat.

Senator Molan did not respond to the accusations on the floor of the Senate.

But in his 2009 book Running the War in Iraq, he said the coalition did "everything we could to avoid killing innocents".

"[Military commanders] did not want to aggravate an already difficult situation, and their first guiding principle was often expressed as the old medical dictum: 'First, do no harm'," he wrote.

"There was a continual search for any approach that did not involve bombs and bullets."

Tensions flare over 'white supremacist' accusation

Coalition senators rallied behind Senator Molan.

Queensland senator Barry O'Sullivan said Greens senator Sarah Hanson-Young had accused Senator Molan of being a white supremacist.

"She's done it twice, it's a despicable thing to say about a fellow senator," he said.

Senator Hanson-Young was unrepentant.

"I said that the senator was supporting white supremacists. That is what he did when he shared that Facebook post," she said.

"That is what he's being asked to apologise for, that is what he should be ashamed of."

Senator Molan shared a Britain First video on his Facebook page. ( Facebook: Jim Molan )

Late on Tuesday, Senator Molan conceded it was "unwise" to have shared the Britain First videos and said he had since shut down his personal account.

"Now that I have my senator's social media in place I have closed down my personal social media," he said in a statement.

"It was unwise to re-post the two videos because they allowed my political opponents to misrepresent me.

"Of course I am not racist, nor anti-Islam, and I do not support Britain First. I am anti-violence and anti-civil disturbance.

"I am part of the most successful multicultural nation on Earth and I am proud of that."

Molan 'doesn't have a racist bone in his body': PM

Senior Coalition frontbenchers have also defended Senator Molan.

Finance Minister Mathias Cormann said Senator Molan was "a great Australian who's provided outstanding public service to Australia".

Prime Minister Malcolm Turnbull told the House of Representatives the treatment of his new senator was "deplorable".

"The Leader of the Opposition wants to describe him as a racist, that is deplorable, it is disgusting," he said during Question Time.

"Jim Molan is a great Australian soldier, we are lucky to have him in the Senate.

"He doesn't have a racist bone in his body."

Labor senator Penny Wong took to social media to critique the Coalition's response.

"Very sad to see Mathias Cormann join Malcolm Turnbull in refusing to condemn Senator Molan over his offensive Facebook posts," she tweeted.

"Hateful and divisive messages do nothing to protect us, they only divide us. They have no place in our society, and no place in our parliament."