Although there is a growing movement within the Labor Party for Kevin Rudd to reassume leadership, current party leader and Australian Prime Minister Julia Gillard has secured sufficient support from powerbrokers. Enough support for her to remain in post amid discontent over her failed Malaysia Solution on border security.

Reports of party discontent came at about the same time that opposition leader Tony Abbott challenged Ms Gillard to resign over her alleged failure to protect the country's borders.

The continuing support for the prime minister is due to a party-wide understanding that Ms Gillard would be given until the end of 2011 to boost the party rating since the first half of the year she devoted to development of the proposed carbon tax amid continuous opposition criticism.

Outside Labor powerbrokers, Ms Gillard has the support also of some independent MPs.

"My support for Julia Gillard is unchanged. Moreover, as I have said repeatedly, my agreement with Julia Gillard is with her personally and I'd be hard-pressed to support a successor if there was a change of leadership," The Australian quoted independent MP Andrew Wilkie.

The call for a change in Labor's leadership was fueled by a claim from former Labor powerbroker Gragam Richardson that 20 MPs from the party are supporting for Mr Rudd's return to the top post.

Coalition senator Nigel Scullion also claimed on Thursday that he heard a phone call three nights ago wherein Mr Rudd allegedly told a Labor senator that the former prime minister lacked only nine votes to return to power.

Labor Senator Trish Crossin confirmed she spoke with Mr Rudd three weeks ago, but said their conversation was not about leadership changes.

Mr Rudd, who celebrated Thursday his 54th birthday in New York attending meetings as Foreign Minister, denied speculations that he wanted to unseat his successor.

The assurance from Mr Rudd is seen as a signal for Ms Gillard to concentrate on seeking more support from crossbenchers for her proposed amendments to the offshore processing bill. So far, four of the crossbenchers - Tony Windsor, Rob Oakeshott, Tony Crook and Bob Katter - have agreed to support Labor's planned changes to the Migration Act, but the House adjourned before a vote could be taken.

Ms Gillard's proposal is to send 800 asylum seekers, who came by boat to Australia, to Malaysia in exchange for 4,000 proven refugees.

Greens leader Bob Brown said the party will support whom Labor will appoint as leader as its coalition partner, but continued to criticize offshore processing.

A poll released last week said that support for Ms Gillard is at a record low, but Labor has chances of improving its rating if Mr Rudd would replace Ms Gillard as party leader.