Archer told ESPNcricinfo that someone claiming to be the same person had contacted him via Instagram.
The England and Wales Cricket Board (ECB) is now investigating, Sky Sports said. Archer reported the message to ECB officials and they passed it on to New Zealand Cricket (NZC).
It wasn’t clear if the message was an apology or further insults, Sky Sports said.
But authorities are confident of being able to identify the person as a result of the contact, ESPN said. NZC had already been going through security footage of the ground.
Chief executive David White earlier vowed to throw the book at the spectator, revealing he could receive a life ban from attending matches in this country.
If found, the person could face criminal prosecution but from a NZC perspective, White intends to push for as severe punishment as possible.
“If we did find the person we’d refer them to the police in the first instance,” White told Stuff. “Secondly, my personal view is that they should never be allowed into a cricket ground in New Zealand again.
Meanwhile, Ashley Giles believes supporters should be helping to weed out troublesome individuals. As the search for the offender continues, Giles, the managing director of the England men’s team, insists spectators can do their bit to stamp out racism by flagging any issues to security at the ground.
Giles said: “I’m sure someone else must have heard it and I hope they come forward. [If] people are sitting next to this and not reporting it to stewards then there is something seriously going wrong with our society.
“We can’t accept that it’s just part of society, it happens in lots of sport, we hear about it daily, and we don’t need it in cricket.
“I’m sure there is a lot that goes on that isn’t reported, unfortunately. There are measures and all sorts of abuse that goes on, I know from my experience, and this is one of those forms that is the worst.”
White apologised to Archer in person on the England team’s arrival into Hamilton on Tuesday ahead of the second Test which starts later this week, where security will be beefed up in an attempt to avoid a repeat occurrence.
Stuff with PA