England face a colossal target of 658 to win the third Test after Kane Williamson's century on Monday rammed home New Zealand's advantage with more than two days remaining.

Williamson posted a 33rd ton to continue a career glut of runs at Seddon Park before departing for 156 as the home side were dismissed for 453 late on day three.

Daryl Mitchell scored 60 and Mitchell Santner 49 not out, setting up the prospect of a consolation New Zealand win after they were well beaten in the first two Tests of the three-match series.

England's hopes were dealt a blow by a hamstring injury to captain Ben Stokes while he was bowling midway through the second session.

The 33-year-old limped from the field in pain and he is in doubt to bat in the fourth innings.

The opening session was lost to rain in Hamilton but Williamson quickly found his methodical groove after resuming on 50.

He put on 105 for the third wicket alongside Rachin Ravindra, who was caught for 44 off a leading edge from seamer Matthew Potts.

Williamson departed soon after powering New Zealand to 274-4 at tea, top-edging a sweep into the deep of Shoaib Bashir (2-170).

New Zealand's greatest run-scorer struck 20 fours and one six as he took his career tally of Test runs at Seddon Park to 1,614, the most by any batter at any New Zealand venue.

He has scored centuries in five successive Tests at what is his domestic home ground for Northern Districts, where he boasts an average of 94.94 from 21 innings.

Williamson survived a tight Brydon Carse lbw appeal review on 73 and was later dropped by wicketkeeper Ollie Pope, when a difficult leg-side chance spilled from his glove off Stokes.

Mitchell was caught in the deep to hand part-time spinner Jacob Bethell a first Test wicket and, ultimately, England's best bowling figures for the innings of 3-72.

Santner also holed-out off Joe Root to fall just short of back-to-back half-centuries for the match.

Veteran seamer Tim Southee, who is playing his 107th and final Test, only scored two in his last Test innings.

He failed to add to his career tally of 98 Test sixes, leaving him ranked fourth on that list.

Earlier, overnight rain continued into the morning, forcing match officials to abandon the first session.

New Zealand resumed on 136-3, holding a 340-run advantage after the tourists were skittled for 143 on Sunday.