Williamson, who grew up and still lives near the Bay Oval in Tauranga, said he was shocked to hear about the incident and that neither he nor his teammates were aware of it until Archer tweeted about it on Monday night.
New Zealand prides itself on its multicultural society and has, as ever, provided a warm welcome to the England team. But Williamson wants to apologise on behalf of all New Zealanders when the sides meet again in Hamilton in the coming days and try to ensure "nothing like that ever happens again."
"It's certainly against everything that we as Kiwis are about, and I certainly hope that nothing like that ever happens again," Williamson told Stuff.co.nz. "I can only apologise on behalf of Kiwis to Jofra, not only from our team and how we look to conduct ourselves, but what we expect of Kiwis in general.
"It's a horrific thing. In a country, and a setting where it is very much multicultural, it's something we need to put to bed quickly and hope nothing like that ever happens again. It certainly won't if there's any influence we can have on it.
"Was I shocked? Absolutely, 100 percent. I will try see him over the next few days if I can, definitely."
New Zealand Cricket also released a statement confirming it would officially apologize to Archer and reiterating the zero-tolerance attitude to such incident.
"NZC has zero tolerance towards abusive or offensive language at any of its venues and will refer any developments in the case to police," they said.
While CCTV footage has so far been unable to identify the perpetrator, Archer believes he was contacted by the same individual on social media on Monday night. He has since provided details to the relevant authorities.