Archer, 24, says he heard comments from "one guy" at the Bay Oval in his side's defeat by an innings and 65 runs.

"I found the incident a real shame," Archer wrote in the Daily Mail.

"If someone wants to shout at me and tell me I'm bowling badly - that's fine. To hear racism, though, that's another matter."

He continued: "There is no time or place for it in any walk of life, let alone cricket. It's just not called for."

The England and Wales Cricket Board (ECB) said it is investigating the incident, which took place while Archer walked off the field following his dismissal in the second innings in Mount Maunganui.

As part of the investigation, England revealed the Sussex paceman had received a direct message via social media from someone who is alleged to be the culprit.

"It's emotional, it hurts and we fully support Jofra," said England's director of men's cricket Ashley Giles. "He is a young man making his way in the game and we don't need that sort of distraction."

New Zealand captain Kane Williamson later said he would apologise to Archer in person for the racist abuse he was subjected to.

"It's against everything that we as Kiwis are about," Williamson told stuff.co.nz. "I certainly hope nothing like that ever happens again.

"It's a horrific thing. In a country and a setting where it is very much multi-cultural, it's something we need to put to bed quickly."

The second Test begins in Hamilton at Seddon Park on Thursday (22:00 GMT).