The two appeared face to face in a Sky Sport UK show called Gloves Are Off where Whyte called out Parker for his failure to be more aggressive in April's world title fight with Anthony Joshua.
The fight went the distance with Joshua winning by unanimous decision.
Whyte, whose only defeat is by TKO to Joshua, described Parker's performance in the latter stages of the bout as 'cowardly'.
"His performance was cautious but it was also cowardly as well," Whyte said.
"I understand it's a big fight and he needs to be cautious but six or seven rounds into the fight, you're in the home fighter's country, where the champion is a golden boy. Six or seven rounds in you know you'll be down on the scorecards, there comes a time when you've got to go after it and I just feel he was too much of a coward to make the decisions he needed to make."
Whyte compared Parker's performance to his own against Joshua where he claims he fought on despite injuring his shoulder in the second round.
"That's why I think he was a coward. He wasn't hurt at any point in the fight. Didn't get stung or anything but he didn't want to make the decisions to go after him."
Whyte also claimed that Parker let down New Zealand with his performance.
"He had his whole country over, doing the haka. And then he let them down. He didn't show the warrior spirit or warriors courage of what I expect of him, from where he's from."
Parker responded that he fought the better Joshua, with his bout occurring two years after Whyte's clash against his compatriot. The Kiwi said it was a bad move for Whyte to accept a fight against him.
"I feel that he's so close to it [a world title shot] that he's going to take the wrong fight and lose it all. I feel I have better speed, better movement. Whenever I'm in a fight I'm always confident I'm going to win."
When Parker landed in London earlier this week he said he was expecting some Whyte mind games.
"He likes to play mind games and he's very good at talking. He tries to say things to get in your head. Sometimes it's rubbish that comes out of his mouth. But I respect him and let him say whatever he wants to say. But when we get in the ring I want to bash him."
The exchange:
Whyte: "You're desperate now. You let your family down, you let your country down.
Parker: "I didn't let anyone down. I'm set for life," Parker said.
Whyte: "And that's your mindset. You're set for life. Just don't be a coward in the fight. I'm coming for you."
Parker: "Who's the coward?"
Whyte: "You."
Parker: "A coward is someone or calls someone else a coward."
Whyte: "No. A coward is someone who doesn't shoe courage when they need to show courage."
Parker: "Well who got knocked out?"
Whyte: "Because I wasn't a coward. That's why."
