Bangladesh, seeking their first win against a major country, set New Zealand 317 to win the first Test after the home team were bowled out for 242 in their second innings here on Monday.
New Zealand reached seven without loss at lunch on the fourth day and must now bat out the last two sessions today and three on the final day on Tuesday -- an overall 154 overs -- to force a draw or put up their best-ever chase.
At the break, openers Jamie How (six) and Aaron Redmond (one) were at the crease.
Earlier, tail-enders Mashrafe Mortaza (44) added an invaluable 40 runs for the ninth wicket with Abdur Razzak (18) and another 22 for the last wicket with Shahadat Hossain (nought) to help Bangladesh set a formidable target.
Resuming at 188-8, Bangladesh's ninth-wicket pair frustrated the New Zealand attack as they prodded their way to consolidate the lead until paceman Iain O'Brien had Razzak caught in the slips for 18.
Mortaza hit seven boundaries during his 87-ball knock and took the lead beyond 300. He was finally stumped by Brendon McCullum off part-time bowler Redmond to finish the home team's second innings.
Left arm spinner Daniel Vettori followed his 5-59 in the first innings with 4-74.
The Black Caps have successfully chased only one target of over 300, making 324-5 against Pakistan at Christchurch in 1994 but their best match-winning chase away from home is 164 for 4 against Australia at Perth in 1985.
They can however take heart from having batted out 135 overs to draw a Test against India in Mohali in 1999.