Labor wants an independent investigation while the Greens want a commission of inquiry into the claims.

Both parties also want an inquiry into whether Mr Porter is a fit and proper person to be a minister.

Mr Porter announced on Monday he could not proceed with his defamation action against the ABC, which first reported the claim dating back to 1988.

The former attorney-general, who outed himself as the person referred to in the story, now serves as industry minister.

Deputy Opposition Leader Richard Marles said there was a need for an independent inquiry now Mr Porter had dropped the legal action against the broadcaster and reporter Louise Milligan.

"The government were touting this court action as the means by which there would be some form of independent inquiry," Mr Marles told Sky News on Tuesday.

"There are very serious allegations. There is a cloud there which should be resolved for everyone concerned, not least for Christian Porter himself."

The ABC will pay the cost of mediation during the defamation case, but no damages will be paid.

"They have been forced by my taking this action all the way to the court door, they have been forced to say they regret the article," Mr Porter said.

Opposition Leader Anthony Albanese told a caucus meeting the minister's action represented a "complete capitulation" rather than a victory.

But a government MP told a coalition party room meeting the incident showed the ABC's "systemic bias" and urged colleagues to "strike while the iron is hot" and seek the ousting of ABC chair Ita Buttrose.

The ABC said it stood by and did not regret its reporting. The story remains on its website, with an editor's note attached.

Australian Associated Press