SYDNEY // The Australian prime minister, Julia Gillard, squashed a challenge by her predecessor, Kevin Rudd, by a convincing margin yesterday - but her problems are far from over. She must not only reunite her Labor Party, bitterly divided and reeling from venomous in-fighting, but also rescue it from the doldrums in time to have a chance of winning the next election, due late next year. Mr Rudd, who Ms Gillard deposed in mid-2010, promised not to initiate another leadership bid after losing a ballot of Labor politicians 31 votes to Ms Gillard's 71. Mr Rudd said he bore no grudge, but colleagues say he could be drafted for another challenge if Labor's popularity did not improve. Political analysts said the party might even look for a third candidate, given how widely Mr Rudd is disliked by his parliamentary colleagues, notwithstanding his popularity with the electorate. Labor's share of the primary vote has sunk to 26 per cent under Ms Gillard - a low for the party. The latest poll, published in The Australian yesterday, gave it 35 per cent, compared with 45 per cent for the conservative Coalition. A Labor victory still seems a distance away, although Mr Rudd is also more popular than the opposition leader, Tony Abbott, who has 34 per cent support. For the Coalition, the leadership battle - and the public bloodletting - has been a gift. As Labor strategists ruefully admit, the opposition has accumulated a wealth of material for an election campaign, including footage of Labor ministers criticising each other's character and ability. Ms Gillard, Australia's first female prime minister, acknowledged that the internal ructions had been "ugly". Addressing voters, she said: "The leadership question is now determined. I can assure you that this political drama is over … I feel impatient to get on with the job of building this country's future." Mr Abbott said she had won only "a stay of execution". And he challenged the independent MPs propping up her minority government to state whether they had confidence in her, "given the devastating critique of this prime minister that we've seen delivered by so many of her own colleagues". Although the cross-benchers will continue support the government, the position of Labor malcontents is less clear. With Mr Rudd's departure to the backbenches, Ms Gillard must appoint a new foreign affairs minister. She also has to decide whether to sack the five ministers who voted against her, or retain them, in the interests of unity. "This whole affair has been very destructive," said James Walter, professor of political science at Melbourne's Monash University. "It's not impossible that Labor could turn the situation around, but it's a big ask. If the poll support is still so low towards the end of this year, there might be people saying 'We can't let this go on'." Others, though, believe the affair may boost Ms Gillard's popularity. She showed grit and resilience under pressure, and yesterday was gracious towards Mr Rudd, who, according to his critics, tried to sabotage Labor during the 2010 election campaign, and thereafter worked to undermine her government. Paying tribute to Mr Rudd, Ms Gillard listed his achievements in public life, including steering Australia through the global financial crisis, apologising to the Stolen Generations of Aboriginal people forcibly removed from their families and being "an amazing advocate of Australia's interests on the world stage". Analysts attribute Ms Gillard's low poll ratings to an effective campaign by Mr Abbott, relentless criticism of her by certain newspapers and a series of poorly judged decisions. The latter have included the notorious "Malaysia Solution" for processing asylum-seekers, which was thrown out by the High Court. Some also believe she has been more harshly judged because of being a woman. "She has not done a bad job with a very difficult set of cards," said Norman Abjorensen, a political scientist at the Australian National University. "But the way she's been treated raises the question of whether Australians are prepared to accept a female head of government, and from what we've seen, we've got a long way to go." Peter Hartcher, political editor of the Sydney Morning Herald, noted yesterday Labor MPs had failed to endorse the candidate with voter appeal. "For a party that is on a steady trajectory to electoral defeat, it was an extraordinary act of steely resolve," he wrote. "Or suicidal madness," he added.