Archer announced on Twitter a few hours after England’s innings defeat that he had heard “racial insults” from a spectator as he headed off the field at the Bay Oval, where he was the penultimate man out on the final day.
New Zealand Cricket is investigating the claim which has shocked Williamson, who intends to personally apologise to Archer if they cross paths ahead of the second Test at Hamilton later this week.
“I will try, over the next few days if I can see him, definitely,” Williamson - who was born and raised in Tauranga, only a couple of miles from Mount Maunganui, where he now resides - told Nine Media’s Stuff website.
“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 certainly against everything that we as Kiwis are about and I certainly hope that 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 and hope nothing like that ever happens again.
“It certainly won’t if there’s any influence we can have on it.”
New Zealand head coach Gary Stead echoed Williamson’s sentiments as he said: “I hope whoever’s done that is found quickly and it’s dealt with. It’s something we don’t condone at all.”
Ashley Giles, in his role as managing director of the England men’s team, is liaising with an apologetic home board as he lamented the behaviour of one individual.
Giles is also keeping tabs on Archer and is convinced the paceman’s England team-mates will rally round him.
Speaking at the team hotel in Tauranga on Tuesday morning, Giles said: “The tweet that went out was obviously emotional, it hurts.
“We fully support Jof, obviously, there is no place for racism in the game, in any game. Jof is part of our team but, whatever the abuse, we’d be absolutely right behind him. He’s a very important part of our team.
“You know what our team is like, they’ll rally round him pretty well I should imagine. But it’s a serious incident. He’s a young man making his way in the game and we just don’t need this sort of thing.
“It’s a problem in sport still, clearly. It’s terrible in this day and age that this sort of thing is still happening and when it does happen and that person isn’t identified much quicker, even by the people around them it’s really disappointing.
“We’re working really closely with New Zealand Cricket and I’ve spoken to their chief executive (David White) this morning.
“They are obviously incredibly concerned that this happened on their patch. At the moment we believe it’s an isolated incident but we’ll know more once the investigation is finished.”
England are heading inland for Friday’s second Test at Hamilton, where New Zealand Cricket has promised increased security on the ground, with Giles revealing that White has also volunteered to step in personally to reassure the team.
“I do know David is travelling down to Hamilton as well to meet the team as they come off the bus,” he said.
“It is very kind of him. It isn’t a New Zealand Cricket problem, the relationship between us and them is very strong, but it’s a nice gesture on his part.
“One person shouldn’t ruin that but it’s a shame that sort of thing is still in our society.”