Deputy Labor leader Tanya Plibersek says the government would be "incredibly small-minded" not to back Kevin Rudd's candidacy for United Nations secretary-general.
Cabinet will decide whether to support his nomination for the job, but Foreign Minister Julie Bishop told the coalition party room it would not be an endorsement.
"It is an extraordinary proposition that the Australian government would not support an Australian for this very prestigious and important role," Ms Plibersek told reporters in Sydney.
Greens Senator Sarah Hanson-Young said there probably is a good argument to support Mr Rudd because he is an Australian.
"But honestly he's burnt so many bridges I can see why people on both his own side of politics, plus on the Liberal side, wouldn't be too keen to see him," she told Sky News.
Senator Hanson-Young would like to see a "woman run the show for a while" instead.
"That's why I think we should be supporting Helen Clark."
