Senator Lambie posted her intention to raise an inquiry by parliamentary committee on Twitter on Tuesday, almost a week after Greens Senator Larissa Waters failed to introduce a bill which wanted an independent inquiry investigate the allegations.

"Unlike the other shots at setting up an inquiry, this is constitutional, it's funded, it doesn't trample of the separation of powers, it's got terms of reference it can actually answer, and it's actually able to pass and get moving," Senator Lambie Tweeted.

Lambie raised Ministerial Standards as a reason for the inquiry, citing in her notice of motion that "[Ministers] will be required to answer for the consequences of their actions" and they "must ensure... that their conduct in a private capacity upholds the laws of Australia and demonstrates appropriately high standards of personal integrity".

"It does not appear that the Prime Minister has taken any significant action to assess whether Minister Porter meets the criteria."

Last week Senator Lambie blocked Waters' bill. When Waters' raised it again on Wednesday Senator Lambie blocked again after her motion was also rejected.

Commentators took to Twitter to call out the move by the Senator, raising questions about her failure to support the Greens Senators inquiry.

Senator Waters said on Twitter she would continue to raise her bill.

"For the third time, I just tried to refer my Porter Commission of Inquiry bill to inquiry, and again Gov, PHON & Jacqui blocked it."