Labor whip Joel Fitzgibbon has already absolved himself, Prime Minister Julia Gillard said over the weekend, but the Coalition maintained that the man tagged as the source of renewed restiveness in government leadership must be sacked.

Mr Fitzgibbon, media reports suggested, has been working secretly to resurrect former Prime Minister Kevin Rudd from oblivion and possibly head the struggling Labor Party anew in hopes of reversing the likely defeat that faces the government in 2013's general elections.

But the allegations were brushed aside on Sunday by Mr Fitzgibbon as he tweeted: "No one does more to support the PM (Ms Gillard) and the government than me."

For Ms Gillard, the Labor whip's declaration was quite sufficient as she stressed that Mr Fitzgibbon's "words speak for themselves."

She, however, refused to delve further on the issue that the Twitter statement failed to squarely deny the rumours that members of the Labor Party were again agitated by the possibility that Mr Rudd could soon re-emerged as the more viable alternative leader for the ruling party.

"I am looking forward to leading the team into the 2013 election," Ms Gillard told The Australian on Sunday, also dismissing suggestions that she may need to ward off again a likely challenge on her leadership in the days ahead.

Yet for senior Coalition figure Christopher Pyne, Mr Fitzgibbon's recent acts run in counter with that of Ms Gillard's vision, betraying his true identity as not "a 100 per cent rolled gold supporter of the prime minister."

"It is untenable for Joel Fitzgibbon to remain as the chief government whip," Mr Pyne was reported by the Australian Associated Press (AAP) as saying on Monday.

He called on Ms Gillard to ease out Mr Fitzgibbon from his present role as doing the otherwise would leave an impression that "the government is falling apart at the seams."

In an earlier statement, Opposition Leader Tony Abbott said on Sunday that what Mr Fitzgibbon had done actually unmasked the unsettling reality that "the faceless men who run the Labor party are now yet again reconsidering the question of the leadership."

And the Labor whip "has not actually denied the story," Mr Abbott told The Australian in insisting that Ms Gillard should be wary by Mr Fitzgibbon's online statement, which he added merely expressed a vague statement of support for the Prime Minister.

The latest tension within Labor, Mr Abbott said, has become worrisome as Ms Gillard is yet again distracted by nagging questions of her hold in the government.

"As long as the Labor party is focused on itself, it is not getting on with the job of governing our country," the Liberal headliner said.