"This is a case about insults between two men," said Musk's attorney, Alex Spiro, in his opening statement to the jury in a federal courthouse in Los Angeles on the first day of the trial, BBC reported on Wednesday.
Musk said the "pedo guy" tweet was not meant to be taken literally.
The Tesla co-founder filed a declaration that "pedo guy" is a common insult in South Africa used to insult demeanor and appearances.
He elaborated by saying, "It's quite common in the English speaking world. Calling someone a 'pedo guy' means creepy. If you did a search or asked someone what it means it would be a creepy."
Tesla CEO apologised directly to the cave diver in court, looking directly at him.
"I apologised in a tweet and again in the deposition, and I'll say it again - I apologise to Mr Unsworth," he said.
Meanwhile, Lawyers for Unsworth argued that Musk was using his social media platform to damage the explorer's reputation and paint him as a pedophile.
Last year, twelve boys and their coach were trapped in the Tham Luang cave complex, were rescued after a week-long intense drama.
Musk offered to assist the rescue mission by providing a submarine but the request was turned down on the ground that it would be unworkable.
Unsworth took on Musk in a widely-shared interview, saying the "mini-sub" "just had absolutely no chance of working".
In response, Musk tweeted several things, now-deleted, "Sorry pedo guy, you really did ask for it."
Then, a month later, he called Unsworth a "child rapist" in an email.
Unsworth sued two months later in a Los Angeles federal court, saying Mr Musk falsely branded him a paedophile and child rapist.
( With inputs from IANS )