Australia and New Zealand played the inaugural day-night Test in Adelaide last year, attracting huge crowds to rival those at limited-overs versions of the game.
But players from both sides complained about the pink ball, intended to be more visible under floodlights, and some conservatives felt it undermined a Test tradition dating back to 1877.
White said there was strong enthusiasm for more day-night Tests at a meeting of the International Cricket Council board in Dubai last weekend.
"I think the players will be very supportive going forward, (day-night Test cricket) is essential for the survival of the format, to be honest," he told Radio Sport.
White said day-nighters would never dominate Test cricket but he could envisage a time when most series included a match played under lights.
"It provides an opportunity for the game to be more accessible to the fans and we've got to listen to them, they drive the revenue, they drive the game," he said.
Players raised concerns after the Adelaide Test about the pink ball's movement and durability, as well as the difficulty batsmen faced seeing it under lights.
- 'Guinea pig' -
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Black Caps coach Mike Hesson said "fine tuning" would solve the problems, insisting New Zealand's players backed the concept of day-night Tests.
"I think it's inevitable that we'll play a lot more day-night cricket over the coming years," he told reporters.
However, White said Indian officials had "jumped the gun" in announcing last week that they would play a pink-ball Test against New Zealand when the Black Caps tour later this year.
He said administrators in India saw it as a way to raise the profile of Test cricket.
"They realise that they have got an issue with their crowds at Test match cricket," he said.
"While T20 and one-day cricket is huge, they do struggle to get big crowds for Test matches."
Hesson denied administrators in Australia and now India were using New Zealand as a "guinea pig" to trial the effectiveness of day-night cricket before adopting it against big-name opponents.
"To play in front of a full house in India in a Test match would be pretty special," he said.
