The Abbott government has called on new Opposition Leader Bill Shorten to show Labor has learnt the lessons of the September 7 election.
"The first responsibility Mr Shorten has is to ... vote to abolish the carbon tax," junior minister Jamie Briggs said of the Labor leader's first "test".
If he didn't it would show that Labor had not learnt the lessons of the party's rejection by voters.
But the Australian Greens want a Shorten-led opposition to stand by a price on carbon, introduced by the Gillard government in July 2012.
"Look forward to working with you to maintain price on carbon," Greens leader Christine Milne tweeted shortly after Mr Shorten's election.
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Mr Briggs insisted Labor also owed the Australian people an apology for changing border security laws, calling on the opposition to help the government legislate new laws.
"Finally he should ensure that the new opposition passes measures to ensure that we can get the budget back under control."
Mr Briggs took a swipe at Mr Shorten's role in bringing down prime ministers Kevin Rudd and Julia Gillard.
"I just hope for Mr Shorten's sake that the Labor caucus is more loyal to the new leader."
Ms Gillard was one of the first to congratulate the new Labor leader, notwithstanding his controversial role in her dumping in June.
"Congratulations to Bill Shorten on becoming Labor leader. A great honour! I wish Bill all the best. JG" she tweeted.
