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"It starts to sound a little bit - and take this the right way, Donald - like you're a guy with a schoolyard crush. Where we're in elementary school or junior high school, guys often say the meanest things about the girls they like the most," Lauer said.
Trump, a real-estate magnate and GOP presidential candidate, insisted that was not the case.
"Trust me Matt, there is no crush. That I can tell you," he replied.
Trump has repeatedly gone out of his way to criticize Kelly since she moderated the first prime-time debate of the presidential race. Kelly asked Trump a series of questions he later described as unfair, including one about derogatory comments he has made toward women.
Most recently, Trump leveled a number of broadsides against Kelly on Monday night, after she just returned from a vacation. Among other things, Trump declared that "The Kelly File" show was better without her and shared a message on Twitter that called her a "bimbo."
But Trump denied to Lauer that Kelly has somehow bothered him to an extreme level.
"You tweet a few tweets - or retweets, in this case - that's not getting under your skin. I personally am not a fan. I don't think she does a good job. I don't think she's a very good professional. And I think, frankly, the show's better without her. But that's up to them and they can do whatever they want," he said.
He nevertheless continued to blast her supposedly biased moderation of the debate.
"During the debate, she asked me questions that were totally inappropriate. Other people asked nice questions about jobs, about God, about other things," he said. "And she hits me with questions that were totally inappropriate. A lot of people said that."
NBC/screengrab
After Trump's Monday tweets, Fox News appeared to end the previous ceasefire it struck with the real-estate developer. That truce was brokered on August 10, when Fox News Chairman and CEO Roger Ailes reached out to Trump following a particularly controversial comment he made about Kelly that was widely interpreted as a sexist reference to menstruation.
At the time, both sides indicated that they had buried the hatchet. However, with the latest salvo, it seems the feud is back on.
"Donald Trump's surprise and unprovoked attack on Megyn Kelly during her show last night is as unacceptable as it is disturbing," Ailes said in a Tuesday statement. "Megyn Kelly represents the very best of American journalism and all of us at Fox News Channel reject the crude and irresponsible attempts to suggest otherwise."
But Trump said on Wednesday that he still holds Ailes in high regard.
"I respect Roger Ailes. He can do whatever he wants," he told Lauer. "I don't care."
Watch his interview on NBC's "Today" show below: