New Zealand were all out for 254 in their first innings on day three of the second Test, trailing England by 211 at the Basin Reserve in Wellington on Saturday.
Tea was taken at the fall of the last wicket and England gave no immediate indication whether they would force the
follow-on.
Brendon McCullum top-scored for New Zealand with 69 and BJ Watling made 60. England's Stuart Broad took six for 51.