Jofra Archer had said that he would be fine if someone criticised his bowling but believed there was "no time or place for racism in any walk of life".
Resuming the day at 39/2, England were off to a safe start and did not lose a single wicket in the morning session. Joe Root and Rory Burns scored century.
England had earlier bowled New Zealand out for 375. However, the Kiwis struck with two quick wickets at the dying parts of the day to take control.
Notably, Jofra Archer on Monday took to social media to share the information that he was racially insulted by a fan present at the stadium.
The England and Wales Cricket Board (ECB) said England coach Chris Silverwood would depart on Saturday after day two of the second Test in Hamilton.
However, the Barbados-born English pacer Jofra Archer refused to open up about the exact words that he was targeted with.
New Zealand Cricket said in a statement that it intends to apologise to Archer on Tuesday and Black Caps coach Gary Stead believed some of his players would also contact the England bowler.
Both scored Test bests with Watling posting 205, beating his 142 not out against Sri Lanka, while Santner scored 126 to surpass his 73 against Bangladesh.
At Stumps on Day 3, New Zealand were 394/6 with BJ Watling and Mitchell Santner batting on 119 and 31 respectively at the Bay Oval.
In the first Test at the ground, the Bay Oval wicket showed signs of becoming unpredictable late on day two.
