Birmingham - New Zealand were 51 for two, needing a further 193 runs to reach their victory target of 244, when rain stopped play at 3.40pm local time (1440GMT) in their Champions Trophy Group A match against Australia at Edgbaston on Wednesday.
Kane Williamson was 18 not out and Ross Taylor unbeaten on nine.
Only 15 overs had been bowled in New Zealand's innings thus far, with a minimum of 20 required to allow either side to win this match.
GALLERY: WAGs of the ICC Champions Trophy
Defending champions Australia made 243 for eight with Adam Voges top-scoring with 71 and stand-in captain George Bailey, who won the toss, 55.
Australia were without both captain Michael Clarke, following a recurrence of the star batsman's back injury, and opener David Warner, dropped as a disciplinary measure for a bar-room attack on England's Joe Root in the early hours of Sunday morning following their 48-run loss to England at Edgbaston on Saturday.