The former Rockets coach, now a TV analyst, fired the opening salvo last week by declaring that Harden is "not a leader." Harden responded by calling McHale a "clown" and questioning his character.
"Calling me names is not going to change my opinion as to what I saw when I was there," McHale said Friday on TNT. "It's hard to have a lot of credibility if you don't play good defense."
McHale remained complimentary of Harden's basketball skills while explaining what he considers to be leadership.
"He's a hell of a basketball player, he really is," McHale said. "And to James' credit, I will say this: He organizes guys in the summer. He does a lot of stuff. He does a lot of those things. When I was talking more about leadership is ... it's a tie game at half. It's a playoff game, or you're playing another team that's tough and rumble, and they're going to get after you. And all of a sudden, with four minutes to go in the third, you're down nine. They're getting every loose ball, they're getting every rebound, they're doing this stuff. It's not about skill at that point. It's about will. I gotta impose my will on you.
"James at that point gets a little bit -- that's not his personality. Chris Paul, in turn, will get in your face, go nose-to-nose with you, say, 'Hey, let's go,' and I think that's what you need. Draymond Green does a great job, whenever you need a spark. He's out there going jawing with somebody."
Houston acquired Paul during the offseason, and McHale has praised the move because of Paul's leadership abilities.
"Chris Paul will have that leadership at those times where [Harden] gets a little bit introverted, a little bit quiet," McHale said Friday. "You saw the game with the Spurs; he gets to the point where he's just passive. And Chris Paul's not like that."
McHale coached Harden for three-plus seasons in Houston.
"He's a clown, honestly," Harden said after the Rockets' open practice last Saturday, in response to McHale's initial comments. "I did anything and everything he asked me to do. I've tried to lead this team every day since I stepped foot here in Houston. To go on air and just downplay my name, when honestly he's never taught me anything to be a leader ...
"But I've done a great job. The organization, my coaches, you can ask any of those guys how I've worked extremely hard every single day to better [myself], obviously as a basketball player, but be a leader as well. To go on air and downplay my name like that, it just shows his character. I usually don't go back and forth on social media with anybody or with interviews, but I'm going to stand up for myself, and there it is. But you just don't go and do that. It shows what type of person he is."
McHale was fired in November 2015 despite being only 11 games into a four-year, $12 million contract he received in the wake of the Rockets' trip to the Western Conference finals the previous season. Harden believes that bitterness about the firing played a significant role in McHale criticizing him.
"Sure. And I had nothing to do with it," Harden said. "I'm just here to do my job, compete at the highest level I can. But when you're here, you're face-to-face, and you're telling me one thing -- how great of a player you are, how you're lucky that he's able to be a part of this process -- and then you go back just a few years later and basically just say the opposite, it just shows your character, shows who you really are.
"I'm not that type of person. I don't operate that way. I don't say things to somebody behind their back or tell them one thing or go on air and say another thing."
Information from ESPN's Tim MacMahon was used in this report.