Prolific New Zealand batsman Kane Williamson was on Tuesday ruled out of the second Test against India as he continues to recover from a groin strain.

The former captain was included in the tour squad, but delayed his departure and missed the first Test in Bengaluru, which New Zealand won by eight wickets.

New Zealand head coach Gary Stead said in a statement that Williamson was making progress, but was still not ready.

"We're monitoring Kane and he's tracking in the right direction, but isn't yet 100 percent fit," he said.

"We're hopeful to see further improvement over the coming days and have him available for the third Test.

"We'll give him as much time as possible to get himself ready, but certainly continue to take a cautious approach."

The second Test begins on Thursday in Pune.

Williamson, who is New Zealand's greatest Test run-scorer, experienced groin discomfort during the second Test against Sri Lanka in Galle last month.