A Labor win in Melbourne and the national police clearing her office of any involvement over the leaked Kevin Rudd video clip were definitely good kicks to start a new week for Prime Minister Julia Gillard.

Besieged by fresh speculations of leadership challenge within Labor, Ms Gillard got a much-needed breather over the weekend as Labor trumped the Greens in the Melbourne by-election, which was shortly followed by a favourable notice from the Australian Federal Police the day after.

After months of investigating into the embarrassing outtake video cuts of Mr Rudd ranting and swearing while taping a speech, the AFP said computer traces conducted on the matter did not lead to any personalities or offices that can be attributed to the prime minister.

Instead, the national police agency declared that it is pursuing possible clues that reportedly could unmask two likely sources of the Rudd video, which was posted on You Tube days before Mr Rudd's failed attempt to unseat Ms Gillard as Labor leader and PM.

The Daily Telegraph reported on Sunday that the AFP has cleared Ms Gillard or any of her staff of possible involvement in the matter, its eyes focused on two suspects - the one who uploaded the clips online and the other who pilfered them from a hard disk that was said to belong from Mr Rudd's Canberra office.

The likely culprit, The Telegraph said, was a political operative from the New South Wales Labor branch.

Quickly enough though, the NSW Labor Party said in a statement that the Rudd clips "had absolutely nothing to with the NSW branch in any way shape or form."

"The answer is unequivocally no," a representative of the party branch told the publication on Sunday.

The double news came out as Ms Gillard again was left parrying insinuations that Labor's support for her tenure was disintegrating and key party figures have shifted their support to Mr Rudd, deemed more popular and more able to lead the ruling the party come the national election in late 2013.

But senior Labor member Craig Emerson took the cudgels for the embattled Ms Gillard by calling on his party mates to focus on governance instead and drop talks that only distract Labor from governing effectively.

"I think people should knuckle down, back in reform in government, back in the true opponent and that is Tony Abbott, who would bring Australia back to the dark ages," The Australian reported Mr Emerson as saying on Monday.

He stressed too that "it's the right time now for all progressive people, all Labor people, to back in the Prime Minister of Australia."

Another senior cabinet member, Communications Minister Stephen Conroy, warned that the Labor government would only collapse in the event of a Rudd return.

Also, the Australian Greens appealed on Labor elements to heed the call of the Australian public for "stability and a parliament that runs its full term."

Greens MP Adam Bandt said in an interview with News Ltd that Labor powerbrokers were effectively destabilising the government by "white-anting the prime minister."