Prime Minister Julia Gillard edged closer to retaining power in Australia on Thursday when an independent lawmaker said he would support her centre—left Labour Party to form Australia’s first minority government in almost seven decades. A bloc of three independent kingmakers will now decide whether Labour will govern for a second three—year term or whether a conservative Liberal Party—led coalition will form the next administration after August 21 elections failed to give any party a majority.

The conservative coalition now needs the backing of all three remaining uncommitted independents to reach a 76—seat majority in the 150—seat House of Representatives, while Labour needs only two.

Independent Andrew Wilkie announced his decision to back Labour after meetings with Ms. Gillard and Liberal leader Tony Abbott, whose party represents the conservative spectrum in Australian politics, despite its name.

“I have judged that it is in fact the ALP that best meets my criteria that the next government must be stable, must be competent and must be ethical,” Mr. Wilkie told reporters, referring to the Australian Labour Party.

Mr. Wilkie became a lawmaker after quitting his job as a defence intelligence analyst in 2003 to protest the then—conservative government’s “grossly unethical” explanation for sending 2,000 Australian troops to back U.S. and British forces in the Iraq invasion.

Mr. Wilkie said he expected his fellow independents, Bob Katter, Rob Oakeshott and Tony Windsor, were now more likely to support Labour after new figures showed that the coalition had overstated savings from their election promises by up to 10.6 billion Australian dollars ($9.7 billion).

“I did take that into consideration,” Mr. Wilkie said. “I thought that was unacceptable that the alternative government of this country would be out by so far and it did strip away a little bit of the confidence I had developed in Tony Abbott.”

Ms. Gillard accused Mr. Abbott of campaigning “deceitfully” by underestimating the costs of coalition policies and failing to submit most of them to the Treasury and Finance Department for review until after election day.

She said the independent trio had “done the nation a great service” by demanding to see the official costs of both parties’ election promises before deciding whom they would support. The three lawmakers made the figures public late Wednesday after briefings by senior government officials.

“During the election campaign, many Australians were asking themselves what Mr. Abbott had to hide; why he wasn’t putting his policies in for proper costing,” Ms. Gillard told reporters.

“Now, of course, we know he had 11 billion reasons why he wanted to keep these costings a secret.”

Senior Liberal lawmakers have stuck by the accuracy of their own figures and said the discrepancies with official calculations by government ministries were “a difference of opinion” on methodology and underlying assumptions such as future interest rates.

Mr. Abbott said the discrepancies did not compromise his negotiations with the three kingmaker legislators.

“There are a whole lot of issues in play here and, at times, arcane argument about costings is by no means the most important,” Mr. Abbott said. “The bottom line is that there are two competing economic records here.”

He said that when Labour was elected in 2007, it had inherited AU$60 billion ($55 billion) in assets, which it turned into AU$90 billion ($82 billion) of debt through economic stimulus spending.

Treasury documents contradicted Mr. Abbott’s claim that Australia’s bottom line would be AU$11.5 billion ($10.5 billion) better under his conservative coalition in three years, when both sides of politics have promised to return the budget to surplus.

The Treasury found that the improvement could be as little as AU$900 million ($820 million).

It found that Labour had understated the improvement to the budget position under Labour’s policies by AU$62 million ($56 million).

Mr. Windsor described the official figures as “not a good thing for the coalition” before the independent trio began policy discussions on Thursday with lawmakers from both major parties.

Australia will return to the polls if neither leader can secure the support of 76 lawmakers. Australia has not had a minority government since 1943.

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