Unsworth had declared that Musk could "stick his submarine where it hurts", prompting the billionaire to take to Twitter and call him a "pedo guy" to his 22 million-plus followers.
The lawsuit says that with that tweet, Mr Musk sought to tell the average reader that Mr Unsworth's failure to sue at the time was evidence that he was a paedophile. Later Musk accused Unsworth of moving to Thailand to be with a bride who was about 12 years old.
Musk initially apologized for his words toward Unsworth, tweeting that his "actions against me do not justify my actions against him", adding that "the fault is mine and mine alone".
Mr Unsworth was part of the team of global divers who became known worldwide after they successfully rescued all 12 youngsters and their football coach when they became trapped for two weeks by rising waters in a Thai cave complex.
In a series of tweets on July 15, Musk, who personally delivered the submarine to the cave, wrote that he never saw Unsworth and challenged him to show a video of the final rescue.
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"I suggest that you call people you know in Thailand, find out what's actually going on and stop defending child rapists, you f****ing a**hole".
Mr Unsworth filed the suit in California.
The filing also says Mr Unsworth is seeking "punitive damages" as well as the compensation, "to punish him for his wrongdoing and deter him from repeating such heinous conduct".
Then in a second email to BuzzFeed, he accused Unsworth of being a liar and said he was not on the cave dive team.
He resurfaced the controversy earlier this month saying it was "strange" that Unsworth had not sued him over the comments. He was offered free legal services.
Unsworth said he has been exploring caves since 1971, when he was 16, and now shares a house in the Thailand countryside near Chiang Rai with a 40-year-old woman who owns a nail salon.