Henry Nicholls took advantage of a brief dry spell to reach his sixth test half century before rain forced the players from the field after about 10 minutes of play in the first session with New Zealand on 233 for four.
Nicholls, who had resumed on 49, clipped a Jimmy Anderson delivery off his hip for two runs to bring up the mark.
He then almost ran out batting partner BJ Watling while taking a quick single. The wicketkeeper, however, was fortunate that the throw from Chris Woakes was wide.
Watling was on 18 and Nicholls 52 when rain, which had washed out almost the entire second day, forced the players off again.
Officials tried to restart play on several occasions but the rain kept returning as they were making pitch inspections or while groundstaff were preparing the outfield.
Play was eventually abandoned at about 6:45 p.m. (0545 GMT).
The hosts had bowled England out for 58 on the first day.
Rain is forecast for much of the remainder of the match, the first day-night test in New Zealand.
The second test, a standard daytime match, is at Hagley Oval in Christchurch from March 30-April 3.
BRIEF SCORES: England 58. New Zealand 233 for 4 (Kane Williamson 102, Henry Nicholls 52 not out)