Rudd replaced former prime minister Julia Gillard in a Labor party vote on Wednesday after successive polls predicting a Labor government washout at the next election.
The Galaxy Research survey, the first national poll published since the leadership change, showed Rudd well ahead of conservative opposition leader Tony Abbott as preferred prime minister by 51 percent to 34 percent, with 15 percent undecided.
However, Labor's vote still lagged behind the opposition by 49 percent to 51 percent on a two-party' basis, meaning if a vote was held now the conservative opposition would still win. The gap had narrowed sharply, with Labor gaining four percent from the last poll, conducted earlier in June.
Rudd has yet to announce any new policies, but the Mandarin-speaking former diplomat has highlighted the difficulties Australia faces with "the end of China's resource boom", which has underpinned years of economic growth.
Abbott has promised to scrap a Labor government imposed carbon tax and 30 percent tax on iron ore and coal mine profits if he wins power.
Abbott has criticized Labor for dumping a prime minister in party room ballot, but opinion poll respondents overwhelmingly thought Labor had been right to replace Gillard with Rudd.
Gillard has announced she will now quit politics and a string of ministers have resign. Rudd's new ministry is due to be sworn in on Monday.
The Galaxy poll was conducted immediately after Rudd defeated Gillard. It was published in News Limited papers on Sunday.
(Reporting by Christopher McCall; Editing by Michael Perry)
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