Mr White has written to acting Speaker Mary Porter to object to comments made by Mr Hanson this month, including claims that the ACT Labor Party had called for "reinforcements" to help convince the public about the merits of the $783 million project.

Mr Hanson told the Assembly that Labor had brought Mr White to Canberra from Melbourne earlier this year because it was struggling to sell the tram politically.

He said the unions peak body secretary should instead be advocating for workers' rights.

"We know that Mr Alex White has been brought up to try and save the struggling Labor Party in their campaign," Mr Hanson told Assembly debate on August 11.

"I have heard back from people that Alex White has gone in and said to them, bald faced, "I've been brought up here to try and shore up the Labor Party's campaign on light rail."

"People have then come back to me and said, "You won't believe what this bloke said to me," Mr Hanson said.

He claimed Mr White had sought assistance and funding from unions including the Construction, Forestry, Mining and Energy Union and was emphasising job creation from the project because its transport and economic credentials did not stack up.

Under rules of the Assembly, individuals or corporations named in official proceedings can seek a written right of reply if they feel they have been adversely affected in reputation, respect, business dealings or had their privacy invaded.

Mr White said his professional integrity and that of "every trade union in the ACT" had been called into question by the comments. He accused the Liberal leader of making "extreme anti-union statements" and abusing his position.

In June last year controversial Canberra identity Jorian Gardner won a right of reply to comments by Mr Hanson and other Liberal members during debate about an Adolf Hitler-themed strip act at the Multicultural Festival fringe event.

Ms Porter will be required to consider the letter requesting a right of reply, before an Assembly committee will decide if it is appropriate. Rights of reply are added to the Hansard record of proceedings.

Mr Hanson was unmoved by the complaint on Thursday.

"Mr White should spend more time focused on the needs of workers and less time on self-promotion and running political campaigns on behalf of the ALP and CFMEU," he said.

The conflict shows no signs of abating.

Volunteers are being rallied to letterbox thousands of homes in Canberra's south with a Unions ACT flyer urging support for light rail because the project will "rapidly create 3500 secure, local jobs from 2016 to 2018."

In a further escalation, next month residents in the newly formed Murrumbidgee electorate will receive pre-recorded phone calls urging them to contact Mr Hanson and ask him to support the 12 kilometre first stage of the light rail, from the city to Gungahlin.

The call will feature an actor reading a script about a Canberra mother concerned about job creation in the ACT.

The recorded message, similar to one used by the CFMEU in July as part of its campaign against the Abbott government's free trade deal with China, will give a phone number for Mr Hanson's office.

Respondents will also be able to leave a recorded message for Mr Hanson which will be transcribed and sent to him.

Rights of reply are rare in the Legislative Assembly, but have been granted to individuals and organisations since 1995.