Lawyers for Senator Pauline Hanson have sent a defamation warning to Independent Senator Lidia Thorpe for claiming the One Nation leader was a "convicted racist," as well as Channel Nine for broadcasting the remarks.

Senator Hanson shared copies of defamation notices on Twitter on Thursday after Senator Thorpe, a Gunnai, Gunditjmara and Djab Wurrung woman from Victoria, called the Queensland Senator a "convicted racist" on Channel Nine's Today Show.

"Senator Hanson gets away with so much. She is a convicted racist," Senator Thorpe said.

"She has worn a burqa in the chamber; she baits me regularly with racial taunts, and what she did to Senator Payman was question her legitimacy in this place."

Senator Thorpe offered no elaboration on what she meant by "convicted racist".

Earlier this month, Senator Hanson was found guilty of breaching 18c of the Racial Discrimination Act for racially discriminatory social media regarding NSW Senator Mehreen Faruqi.

The Queensland Senator told Senator Faruqi - who is Muslim and born in Pakistan - to "p**s off" back to Pakistan.

The judge said Senator Hanson "has a tendency to make negative, derogatory, discriminating or hateful statements in relation to about or against groups of people relevantly identified as persons of colour, migrants to Australia and Muslims, and to do so because of those characteristics".

The ruling was a civil, not criminal, finding.

Senator Hanson's lawyer, Anthony Jefferies from Gillis Delaney Lawyers, said in his letters - both titled "Defamation of Senator Pauline Hanson" - that "no such conviction" against Senator Hanson exists.

"A conviction means being found guilty of a criminal offence, on the criminal standard of proof and being liable for criminal penalties," the letter to Senator Thorpe said.

"It is highly irresponsible of you to have used this language on national television.

"It cannot have occurred incorrectly given how self-evidently false your claim is.

"We require you to immediately and publicly withdraw the allegation that our client stands convicted of a criminal offence and to apologise to her for your inappropriate conduct."

Senator Thorpe told journalists she didn't understand the grounds on which Senator Hanson was proposing potential legal action against her.

"Senator Hanson was taken to court by Senator Faruqi and was found to be racist towards Senator Faruqi, so I'm not sure what she would be suing me for or taking me to court for," she said

In a separate letter to Kiah Officer, legal counsel for the Nine Network, Mr Jefferies said: "It is highly irresponsible of Nine to have broadcast this allegation on national television — uncorrected."

"Senator Thorpe has a reputation of making wild, uniformed allegations - a fact that is no doubt known to the Nine Network," he wrote.

He said Nine needed to withdraw the allegation as well as apologising to the Queensland Senator, arguing it must occur on the Today show on Friday morning.

On Thursday afternoon, a statement from the Nine Network said: "TODAY wishes to clarify that Senator Hanson has not been criminally convicted of racism, and any suggestion to the contrary is unequivocally withdrawn."

The stoush comes after a fiery Senate hearing on Wednesday saw Senator Hanson move a motion to refer WA Senator Fatima Payman for an investigation over an alleged section 44 citizenship issue.

Senator Hanson claimed Senator Payman - who was born in Afghanistan - hadn't provided enough documentation to prove she had revoked her citizenship. Section 44c prevents anyone holding a citizenship of another country from sitting in parliament.

The motion failed and in a separate social media post, Senator Hanson shared a petition calling for the issue to be taken to the High Court.

Afterwards, when asked by reporters if the call to refer Senator Payman by Senator Hanson was motivated by racism, Senator Thorpe said: "Absolutely".

"Anything that comes out of her mouth is motivated by racism," she said.

Senator Hanson was condemned by then Liberal attorney-general George Brandis in 2017 for her calls to ban the Burqa in parliament, arriving in the Chamber wearing the religious garment despite not being Muslim.

"(To) ridicule that community, to drive it into a corner, to mock its religious garments is an appalling thing to do and I would ask you to reflect on what you have done," Mr Brandis said at the time.

In Senator Hanson's first speech as a member of federal parliament, in the House of Representatives in 1996, she claimed Australia was "in danger of being swamped by Asians". At the time, the vast majority of migrants to Australia were from the UK (37 per cent), New Zealand and Europe.

On Wednesday evening, Senator Thorpe was suspended by the Senate until the end of Thursday - the last scheduled sitting day of the year - for her "aggression" and "hateful personal attacks" in recent weeks.

However, she snuck into Parliament on Thursday and declared she was tired of being treated like "the naughty little Black girl" in the Senate before admitting she would "do it all again" when it comes to her verbal stoush with Senator Hanson.