England need 299 runs to win the second Test against New Zealand and seal the three-match series after dismissing the visitors for 284 in their second innings at Trent Bridge on Tuesday.
In-form Daryl Mitchell made 62 not out as New Zealand added valuable runs after resuming on 224-7.
All four results are still possible with a minimum of 72 overs left on an enthralling final day at Trent Bridge.
A win for Ben Stokes's team requires the highest successful run chase at Trent Bridge. The existing record is England's 284-6 against New Zealand in 2004.
Test world champions New Zealand are painfully aware that England have already knocked off the 277 required to beat them in the final innings of the first Test at Lord's.
England are aiming for a first Test series victory since January 2021 as Stokes and new coach Brendon McCullum look to start their reign in style after a gloomy period for the national team.
A dramatic collapse in the evening session on day four had left New Zealand with a precarious lead of 238, giving England unexpected hope of a memorable success.
But Mitchell, unbeaten on 32 overnight, and number 11 Trent Boult (17) put on 35 for the last wicket to leave the match delicately balanced.
England will need to score at over four an over to win, although New Zealand will be without the services of injured pace bowler Kyle Jamieson.
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