Trent Boult isn't ruling out New Zealand's chances of victory in the first test against Bangladesh.

The visitors will start day four on Tuesday with a 73-run first-innings lead with four wickets in hand after reaching 401–6 at stumps on day three in Mount Maunganui.

That put the underdogs in a handy position to dictate terms, particularly if they can add notably to their run tally in the first session on day four at Bay Oval.

But Boult, who took 3-61 off 30 overs of sweaty toil, believes the final result is a long way from being determined, with a NZ win or the more likely draw also possibilities.

'I'm presuming Bangladesh want to bat once and bat big and put a lot of pressure on us,” Boult says.

And the touring side's team director Khaled Mahmud confirmed that after stumps, saying he'd love Bangladesh to get a lead of around 150 before chasing New Zealand second-innings wickets.

The two unbeaten batters, Yasir Ali (11 not out) and Mehidy Hasan Miraz (20 not out) are capable of advancing their side's cause before the tail appears, while the hosts will want to maximise the arrival of the third new ball in four overs.

'If we can start well, take four nice wickets and then go out their positively with the bat, I would agree that all three results are on the card,” says Boult, who complimented the opposition on their impressive efforts over the past three days.

'They played really, really well. I thought they were decisive and obviously made us come back and bowl spell after spell. The wicket is obviously a pretty good one, and it looks like it might go down to the wire.”

Visiting captain Mominul Haque and Liton Das provided the glue which bound their innings on Monday, with Mominul making 88 from 244 balls before falling in the last hour of play while Das followed soon after for 86 as the pair put on 158 for the fifth wicket.

Spin bowling allrounder Rachin Ravindra was required to bowl 26 overs, going wicket-less as the absence of Ajaz Patel looked more regrettable, while regular spearhead Tim Southee was briefly bowling with a 6-3 legside field to Das as New Zealand sought a breakthrough which came late.

As Boult notes, the previous two tests at the venue have been decided late on day five with wins for the hosts over England and Pakistan.

He's hopeful the wicket may deteriorate to help him and his fellow bowlers on day five, but first the home side's batters will need to play their part.

New Zealand 328 versus Bangladesh 401-6 (Mominul Haque 88, Liton Das 86, Mahmudul Hasan Joy 78, Najmul Hossain Shanto 64; Trent Boult 3-61, Neil Wagner 3-98).

-Stuff/Ian Anderson.