New Private Senators' legislation to change the Racial Discrimination Act should be voted down at the first available opportunity, says Australian Greens spokesperson for legal affairs Senator Penny Wright.

"This legislation is fanning the flames of division right when we need to be coming together as a nation," Senator Wright said.

"A groundswell of public opinion has defeated this legislation once and we are confident any proposal to bring it back will also fail.

"The Greens are very proud to have been part of the community campaign against watering down race hate laws," said acting Greens Leader, Adam Bandt MP.   

"The Government's backdown on the 'bigot' laws show that the community can make this Government change direction.

"This victory will give a big boost to everyone campaigning against Tony Abbott's agenda.