In an open letter on Tuesday, Gene Munster, a managing partner at Loup Ventures, said Musk's comment "crossed the line." In a since-deleted tweet, Musk called British diver Vernon Unsworth a "pedo guy" after he criticized the billionaire's proposed submarine rescue plan as a "PR stunt."
"Your behavior is fueling an unhelpful perception of your leadership - thin-skinned and short-tempered," Munster wrote in his letter, which was published on behalf of investors. "I suspect you would agree, given you removed the string from Twitter, but it will take more than that to regain investor confidence."
The exchange between Musk and Unsworth accelerated over the weekend with Unsworth telling media he is considering taking legal action against the Tesla CEO. In the letter, investors urge Musk to apologize, then "focus your message on your progress toward achieving Tesla's mission." That could even involve a Twitter sabbatical, they suggest.
The Tesla and SpaceX CEO has faced mounting scrutiny lately. Earlier this month, Musk criticized the media for "negative" coverage of Tesla, and in May said he would create a site where people could rate the trustworthiness of an article and track journalists' "credibility score." In June, he was involved in a dispute with an artist for allegedly using his work without compensation.
There have also been larger issues involving Tesla. The electric car company has dealt with scandals involvingand .
"Over the last 6 months, there have been too many examples of concerning behavior that is shaking investor confidence," Munster wrote in the letter. "I'm confident that this letter represents the view of investors and customers who want to see you succeed."
Tesla didn't immediately respond to a request for comment.