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Jofra Archer bowled just three deliveries of the 55th over with New Zealand unable to add to their score of 173-3 before rain swept across the area and ground staff rushed to cover the wicket block and parts of the outfield.
Rain is forecast for much of the rest of Friday.
Tom Latham was on 101, while Henry Nicholls was on five when players left the field.
Ross Taylor was the only wicket to fall in the middle session for 53 when he was snapped up at first slip by England captain Joe Root, his third catch of the innings, on the ball after he brought up his 32nd test half century.
The wicket ended a 116-run partnership with Latham after New Zealand had slumped to 39-2.
He also had a nervous wait on 79 after England reviewed an lbw appeal from Chris Woakes that was initially turned down. Ball-tracking technology showed the ball had pitched outside leg.
Jeet Raval (five) and captain Kane Williamson (four) were both snapped up by Root in the slips inside the first hour after Broad and Woakes found some movement off the pitch.
New Zealand won the first match of the two-test series at Bay Oval in Mt. Maunganui by an innings and 65 runs.