The AC Nielsen poll showed that only 27 percent of voters would choose her Labor party first under Australia's system of preferential voting, the first time in the poll's 39-year history any major party has registered under 30 percent.

The conservative opposition would win a thumping majority if an election were held now, it showed, with 59 percent support for the opposition against 41 percent for the government on a "two-party" basis, eliminating votes for minor parties. The result represents a three percentage point gain by the opposition.

The poll also showed that Kevin Rudd, the man she ousted nearly a year ago and who is now her foreign minister, commands nearly twice as much support among the public as potential Labor leader.

It also showed growing support for the Greens, but continued solid opposition to the carbon tax.

Gillard came to power in June last year to become Australia's first female prime minister, ousting Rudd in an internal party coup. She went on to win a wafer-thin majority in a general election, and now governs with a one-seat majority, thanks to the support of independents and one green MP.

Despite this, she is trying to introduce ground-breaking tax reforms, including a watered-down version of the mining tax originally planned under Rudd and the new carbon tax, which is scheduled to come into force in 2012.

The poll results were published on Saturday in The Sydney Morning Herald and The Age newspapers.

Copyright Reuters, 2011