Mr Best used parliamentary privilege on July 7 to accuse Mr Ferguson of inciting gay hatred.

However, Mr Best did not produce evidence to back up the accusation and he has maintained his silence - and a low profile - since then.

Yesterday The Examiner did manage to briefly contact Mr Best by phone, although he simply said "I can't take your call right now" before hanging up.

Mr Ferguson had said he was taking legal advice after Premier Lara Giddings defended Mr Best's speech at a media conference outside Parliament.

However, Mr Ferguson said yesterday that he would not pursue legal action.

Mr Ferguson was scheduled to debate whether same-sex couples should be allowed to marry at the University of Tasmania on July 28.

He said Mr Best's comments had branded him as a "gay hater" and it would be inappropriate to debate the topic.

"The environment around being able to discuss this issue has now become toxic and people who have strongly held views would be demonised for having those views," Mr Ferguson said.

"The subject has deteriorated to such a degree that the debate itself does not look like a positive experience."

Victorian Australian Family Association president Terri Kelleher and Australian Christian Lobby leader Jim Wallace also withdrew from the debate, citing fears of "personal attack and vitriol".

Both had planned to speak against same-sex unions.

Mr Wallace said Mr Best's comments had caused gay activists to demonise Mr Ferguson, Mrs Kelleher and himself.

"It is very likely that we would see some sort of stunt used to demonise ourselves and the organisations we represent, and we are not prepared to (allow) that," Mr Wallace said.

Tasmanian gay activist Rodney Croome, Education Minister Nick McKim and Tasmanian writer Danielle Wood were to put the case for same-sex marriage.

The University of Tasmania said it would go ahead with the debate, but gave no details on who might argue against gay marriage.