Ten New Zealand players and support staff, along with as many West Indies players and support staff - including their T20I captain Kieron Pollard - cleared the second of their three Covid-19 tests on Thursday.
The tests were conducted specifically for the IPL contingent that had arrived from the United Arab Emirates on November 14.
That group is currently undergoing managed isolation and will take one more test next week, after clearing which they can join the rest of their team-mates in the bio-bubble on November 26.
This will leave many of the players in the T20I squad with potentially just one training session ahead of the series opener on November 27 in Auckland. The West Indies players are currently in Queenstown for the first of two T20 warm-ups against New Zealand A.
Earlier last week, they were barred from training for the remainder of their two-week managed isolation after players from two different bubbles had broken Covid-19 protocols in their Christchurch hotel.
This was believed to have "compromised the bubble integrity of the quarantine facility". However, there was no indication that the larger bubble to the outside world had been breached by any of the squad members.
Meanwhile, Kane Williamson and Trent Boult, who were part of the IPL and are also undergoing isolation, were not named in the T20I squad to face West Indies, allowing them to instead prepare for the two-Test series starting December 3.