By Agence France-Presse
Going private would take the company out of the quarterly reporting cycle, making it "free from as much distraction and short-term thinking as possible," Musk said in a blog post.
Musk, who has depicted the quest to build up no-emissions electric cars as an environmental mission, said he viewed going public as "the best path forward," but that a final decision had not been made and ultimately rested on shareholder support.
Shares finished up 11 percent at $379.57 after being suspended for about 90 minutes following a series of Musk statements on Twitter in which he initially floated the idea of going private.
Musk's first tweet said funding was "secured" for a transaction that could value the company at $420 a share.
At that price, the Tesla transaction would be worth more than $71 billion.
A leveraged buyout of this size -- one using debt -- would eclipse by a wide margin the prior record, the purchase for utility TXU Corp. in 2007 by a consortium that included KKR and TPG for $44 billion.
Gains following the tweet added to upward movement on the stock after the Financial Times reported that a Saudi Arabian sovereign wealth fund had built a stake of between three and five percent in the company.
Musk's tweet comes as Tesla faces continued pressure to ramp up output of the Model 3 sedan, its first effort at the middle market.
The billionaire Musk, who owns about 20 percent of the company, said a transaction would not "substantially" alter his stake and that he expected to continue to lead the company if it occurred.
Musk has previously discussed possibly going private as a means to realize long-term growth and accomplish a goal that some Tesla acolytes embrace with near-messianic passion.
Supporters of Musk and the company view him as a visionary akin to Apple co-founder Steve Jobs, while critics have likened him to a "Wizard of Oz" like figure who has yet to turn a profit.
Tesla shareholder Quint Tatro, managing director of Joule Financial, praised the idea as "brilliant," adding that "Musk is tired of dealing with all the challenges of being 'public.'"
The South African-born Tesla chief has courted plenty of controversy.
Last month, he apologized for calling British caver Vernon Unsworth, who helped rescue 12 Thai boys from a cave, a "pedo" -- short for pedophile -- after Unsworth spoke dismissively of the Tesla chief's proposal for bringing the boys to safety.
He has also had a prickly relationship with Wall Street, apologizing last week to equity analysts after refusing to answer questions on a May investor call.
Musk's approach to a possible go-private transaction also went against the grain of many companies that release major news in non-trading hours.
By contrast, Musk made the initial comment on Twitter and then embellished on the remarks in a series of responses to users on the platform.
In its August 1 earnings release, Tesla confirmed output was on track after missing earlier benchmarks as it reported a bigger-than-expected loss.
Shares have rallied strongly since those earnings, but Musk has continued to show a short fuse towards critics, lambasting "short" sellers of Tesla shares -- those who take bets that the stock will fall in value.
Following the company's surge after last week's earnings, Musk took aim again at a short-seller in a reported short YouTube video that likened these investors to Hitler's last days.
Musk amplified this point Tuesday, saying on Twitter that going private "will be way smoother," end "negative propaganda from shorts" and benefit shareholders.
"Am super appreciative of Tesla shareholders," Musk said. "Will ensure their prosperity in any scenario."