The Human Rights Commission has accepted a racial discrimination complaint lodged by crossbench senator David Leyonhjelm.

The Liberal Democrat lodged the complaint over an article by veteran Fairfax journalist Mark Kenny that blasted him over his wish to see section 18C of the Racial Discrimination Act abolished.

The article, published last month, described him as an "angry white male".

"David Leyonhjelm is a boorish, supercilious know-all with the empathy of a besser block," Kenny also wrote.

Senator Leyonhjelm told the ABC that the Human Rights Commission would now write to Kenny and invite him to respond.

"What I'm seeking from Mr Kenny is acknowledgement that what he wrote was unlawful," he said.

"I'm not looking for money or flowers or sympathy or an apology or anything like that. I'm seeking to make a point."

Complaints relating to racial vilification under the Racial Discrimination Act can be lodged with the Human Rights Commission, which will investigate and either dismiss the complaint, or initiate conciliation processes.

If the matter cannot be resolved, it can be taken to court but as of 2014, fewer than 5 per cent of complaints made it this far.

Senator Leyonhjelm said he expected his case to go beyond the conciliation process.

"I wouldn't be at all surprised if Mr Kenny says, 'to hell with you' … it could even end up in the court system," he said.

Indigenous people have lodged the majority of complaints over 18C to date, followed by members of the Jewish community.

Caucasian people have also lodged a small number of complaints, including one man who took offence at the word "Pom". His complaint was dismissed.

But Senator Leyonhjelm has dismissed suggestions these figures mean the law is effective.

"I don't [think] what ends up in court is a very good indication of the effectiveness or non-effectiveness of the law," he said.

"They're not necessarily the most representative."

Mr Kenny provided a statement to the ABC last month, accusing Senator Leyonhjelm of "rank hypocrisy".

"This vexatious stunt not only proves the point of my piece, it betrays the senator's disregard for the real work of the Human Rights Commission," he said.

'The best way to eliminate racism is to let it burst'

Senator Leyonhjelm said he made the complaint to help his case for abolishing 18C, which makes it unlawful for someone to do an act that is reasonably likely to "offend, insult, humiliate or intimidate" someone because of their race or ethnicity.

It was brought in by the Keating government in 1995.

He said his bill would be reintroduced into the Upper House this week, saying, "protecting our feelings" was not the role of the legal system.

"Supressing speech about racism does nothing to eliminate it," he said.

"The best way to eliminate racism is to let it burst out like boil."

Liberal Senator Cory Bernardi has also tabled a private member's bill to remove the words "insult" and "offend" from the Racial Discrimination Act.

Every Coalition backbench senator — with the exception of Victorian senator Jane Hume — signed on, as did seven crossbenchers, including Senator Leyonhjelm.