England, who trail 1-0 in the five-match series after the first game was washed out, had reached 59 for three when the rain started.
The fourth match is scheduled for Cardiff on Saturday and the fifth will be played at the Rose Bowl in Southampton two days later.
Australia fast bowler Mitchell Johnson of one wicket for 20 runs in five overs
Australia, who elected to field, claimed an early wicket when England opener Michael Carberry was run out in the first over of the innings for one.
Kevin Pietersen also struggled to get going before he mistimed the pull shot and was caught at square leg off left-arm pacer Mitchell Johnson for six, while Joe Root perished for 12 falling caught and bowled by Adam Voges.
Jonathan Trott survived a few close shouts for LBW to reach 28 from 41 balls, while Eoin Morgan was on five when the match was called off.
Photograph: Stu Foster/Getty Images
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