Apple suspended all downloads of the Parler app following the attack on the US Capitol on January 6, citing postings on the platform that could incite further violence. Google and Amazon also cut ties with the company.
Speaking to Fox News Sunday, Cook justified suspending Parler, favored by supporters of President Donald Trump.
"We looked at the incitement to violence that was on there, and we don't consider that free speech and incitement to violence has an intersection," Cook said.
Parler sued Amazon on Monday after Amazon Web Services cut off the platform's access to internet servers.
Parler alleged Amazon was violating antitrust laws and acting to help social rival Twitter, which also has banned Trump for language that could incite violence.
In Apple's case, "we've only suspended them," Cook said. "So, if they get their moderation together, they would be back on" the App Store.
Parler's popularity skyrocketed after Twitter permanently banned Trump following the Capitol attack, which Cook called "one of the saddest moments of my life" and "an attack on our democracy."
"I felt like I was in some sort of alternate reality," he said. "This could not be happening."
The day Apple suspended downloads for Parler, it was the top-downloaded app from the App Store in the US.
Google has also banned downloads of the app.
Parler, which launched in 2018, operates much like Twitter, with profiles to follow and "parleys" instead of tweets.
In its early days, the platform attracted a crowd of ultraconservative and even extreme-right users. But more recently, it has signed up many more traditional Republican voices.
"We have an app store that has about two million apps in it," said Cook. "We obviously don't control what's on the internet. But we've never viewed that our platform should be a simple replication of the internet.
"We have rules and regulations and we just ask that people abide by those."