Shares in the car and renewable energy manufacturer soared and then fell after Mr Musk tweeted on 7 August he intended to take the firm off the stock market.
His initial move came after the company announced its biggest net loss to date of $717.5m (£547.6m) for its second quarter to June.
Mr Musk, the firm’s CEO and chairman, has faced growing criticism over his management style and whether the firm can deliver the volumes required to meet demand.
The value of Tesla’s stock has turned him into one of the world’s richest men as investors have bet on its technology becoming increasingly valuable as the world switches from fossil fuels to renewables.
In a statement made on the Tesla website, Mr Musk said: “Earlier this month, I announced that I was considering taking Tesla private.
“Given the feedback I’ve received, it’s apparent that most of Tesla’s existing shareholders believe we are better off as a public company.
“Although the majority of shareholders I spoke to said they would remain with Tesla if we went private, the sentiment, in a nutshell, was ‘please don’t do this’.
“I knew the process of going private would be challenging, but it’s clear that it would be even more time-consuming and distracting than initially anticipated. This is a problem because we absolutely must stay focused on ramping Model 3 and becoming profitable.
“Considering all of these factors, I met with Tesla’s board of directors yesterday and let them know that I believe the better path is for Tesla to remain public.”
Much of the concern about Tesla’s immediate future has been over production of the Model 3, a lower cost electric car which has received advance orders way in excess of what the firm has so far been able to deliver.
By March, some 500,000 deposits of $1,000 had been paid for a Model 3, according to Fortune magazine, and it took until early July until the firm achieved its target of making 5,000 cars a week.
Last week, Mr Musk told the New York Times the past year had been “excruciating”, with the “worst yet to come” in his personal life.
He said he was exhausted after a year of controversy and had been sleeping in Tesla’s factory, to the detriment of his family, friends and health.
He has five children and has been married and divorced three times (twice to and from the same British actress Talulah Riley) and is currently dating the Canadian musician Grimes.
Mr Musk’s late-night tweet about taking Tesla private sparked havoc in the markets and kicked off a federal investigation over concerns it would be seen as manipulating the marketplace.
The Tesla board has told him to focus on production rather than Twitter, especially following his apology after calling a cave diver rescuing the Thai football team a “paedo guy”.
Tesla is also just one of several ventures Mr Musk is involved in. Others include the SpaceX project to develop reusable space transport, and the hyperloop project, to develop a super-high speed land transport network.
Tesla shares, which are listed on the NASDAQ, fell by 0.2% in after-hours trading.