Trent Boult and Colin de Grandhomme made themselves unavailable for selection due to the prospect of further time in bio-secure bubbles and Managed Isolation.
New Zealand built a lead of 238 with three second innings wickets remaining on Monday heading into a delicately poised final day of the second Test against England in Nottingham.
Tom Latham will captain the team for an entire series for the first time in place of Kane Williamson, who suffered a recurrence of an elbow injury in India and will miss both Tests.
New Zealand pacer Tim Southee has attributed his stellar success away from home in the last three years to adapting quickly to foreign conditions and honing his craft with the old ball.
Matt Henry produced a career-best seven for 23 in a spectacular display of pace bowling as New Zealand skittled out South Africa for 95 in two sessions to take charge of the opening Test in Christchurch on Thursday.
All-rounder Colin de Grandhomme struck a belligerent half-century to steady New Zealand in the second Test on Saturday after South Africa's seamers torched the home side's top order during a see-sawing Day 2 in Christchurch.
Captain Tom Latham smashed an unbeaten 186 as New Zealand bounced back from their shock defeat in Mount Maunganui to amass 349-1 on the opening day of the second and final Test against Bangladesh on Sunday.
Iyer is the 16th Indian batter to score a century on Test debut.
Rookie opener Sarel Erwee savoured a maiden century as South Africa dominated day one of the second Test against New Zealand in Christchurch to be 238 for three at the close on Friday.
Bangladesh looked to be closing in on a shock victory over world Test champions New Zealand after Ebadot Hossain's three-wicket burst in the final session of the fourth day reduced the hosts to 147-5 in the opening Test.
New Zealand skipper Kane Williamson will be rested for the second Test against England due to a left elbow injury, with Tom Latham to lead the side in his absence.
Left-arm spinner Axar Patel picked up five wickets to help India grab a handy 49-run first-innings lead on Day 3 of the first Test against New Zealand on Saturday.
New Zealand last toured Pakistan in 2003 for a white-ball series and since then have avoided touring the country because of security reasons.
The declaration may have come a tad too late owing to the team management's assessment of the Green Park pitch as unresponsive but debutant Shreyas Iyer backed his spinners to secure an Indian victory on the final day of the opening Test.
Mustafizur Rahman's three-wicket haul and Mushfiqur Rahim's unbeaten 16-run knock helped Bangladesh defeat New Zealand by seven wickets in the first T20I of the five-match series here at the Shere Bangla National Stadium on Wednesday.
India's Shreyas Iyer once again dazzled on his debut Test, hitting his second 50-plus score of the match to put his team in charge of the opening Test against New Zealand on Sunday.
Images from Day 2 of the first Test between India and New Zealand, in Kanpur, on Friday.
Left-arm spinner Ajaz Patel claimed a career-best 4-16 as New Zealand kept alive its Twenty20 series against Bangladesh after a thumping 52-run victory in the third game, in Dhaka, on Sunday.
A brilliant 49-ball 65 not out from New Zealand captain Tom Latham was in vain as Bangladesh clinched a thrilling four-run victory in the second Twenty20 international and took a 2-0 series lead, on Friday.
India off-spinner Ravichandran Ashwin struck three early blows to put the hosts on course for a series-clinching victory against New Zealand in the second and final Test at the Wankhede Stadium in Mumbai on Sunday.
Devon Conway's unbeaten 92-run knock followed by a sublime bowling performance by Ish Sodhi propelled New Zealand to a massive 66-run win against Bangladesh
New Zealand fielding coach Luke Ronchi says the record target set by India to win the first Test in Kanpur can be chased down, and exhorted his players to take a leaf out of the home side's batting approach.
Images from Day 3 of the first Test between India and New Zealand, at Green Park, Kanpur, on Saturday.
Images from Day 3 in the second Test between India and New Zealand, in Mumbai on Sunday.
Most of the Test squad and staff had been transferred to hotel quarantine where they will warm up for the two-Test series against England
New Zealand spinner Ajaz Patel claimed the rare honour of bagging all 10 wickets in an innings before India demonstrated their own bowling might to take control on Day 2 of the second and final Test at the Wankhede Stadium in Mumbai on Saturday.
Ganguly is hopeful that Virat Kohli's men will bring the World Test Championship trophy home
New Zealand's three-pronged attack could spell trouble for India on a spiced-up track and Will Somerville, who played a gutsy knock in Kanpur, might have to sit out.
New Zealand made as many as six changes for the ongoing second Test, some forced and some rotated ahead of the World Test Championship final against India in Southampton from June 18.
Seasoned off-spinner Ravichandran Ashwin on Monday went past Harbhajan Singh to become the third highest wicket-taker for India in Test cricket, reaching the mark in his 80th match.
The squad will then be trimmed to 15 for the ICC World Test Championship final against India at the Ageas Bowl in Southampton starting on June 18, as per ICC regulations.
Images from Day 4 in the first Test between India and New Zealand, at Green Park in Kanpur, on Sunday.
Two more failures in two home games could effectively mean end of the road for Ajinkya Rahane, who is leading India in the first Test in Kanpur, starting on Thursday.
Captain Kane Williamson returns to the side after missing the second Test
The 29-year-old left-hander was on 117 with Kyle Jamieson on one at stumps at the Basin Reserve.
'There's no secret we're right in the hunt for the World Test Championship final following our two-nil win over India and having Trent and Kane fully fit and focussed for the upcoming series will be crucial.'
New Zealand captain Kane Williamson has withdrawn from the second Test against West Indies and returned home to be with his pregnant wife, coach Gary Stead said on Thursday.
Kane Williamson finished the day 97 not out - approaching his 21st Test century - with Ross Taylor 31 not out and the home team 243-2 .
For Kohli, a trophy-less cabinet doesn't do justice to the champion performer that he has been for a decade.
An unwell Trent Boult skipped the New Zealand cricket team's training session at the Bay Oval in Mount Maunganui on Monday, staying away from the squad as a precautionary measure. The left-arm pacer is among eight players including Ross Taylor, Colin de Grandhomme, Jeet Raval, Mitchell Santner, Tim Seifert, Tim Southee and Neil Wagner, who are attending the first half of the camp that started on Sunday.