It was not immediately clear if Musk, a prolific user of the social media platform, was being serious about quitting his roles.
Musk, who is also the founder and CEO of rocket company SpaceX, and leads brain-chip startup Neuralink and infrastructure firm The Boring Company, said during a conference call in January that he expects to be the CEO of Tesla for "several years".
"It would be nice to have a bit more free time on my hands as opposed to just working day and night, from when I wake up to when I go to sleep 7 days a week. Pretty intense."
Last month, he asked his followers on Twitter whether he should sell 10 per cent of his stake in the electric-car maker, to which the majority agreed. He has sold shares worth nearly $12 billion since.
Global equity markets, including from the U.S., Europe and Asia, rose while oil prices fell on Wednesday, as traders cheered news of ceasefire proposals to de-escalate the ongoing conflict in the Middle East.
Australia's centre-left government has introduced legislation in the parliament to double penalties for fuel price gouging on Wednesday as global supply disruptions due to the Iran war triggered fuel shortages in some rural regions.
Gulf markets ended mixed on Tuesday, with Qatar extending losses while other bourses steadied as investors parsed conflicting signals on potential US-Iran talks.
Australia and the European Union on Tuesday signed a trade deal marking the culmination of years of negotiations, as Europe seeks to diversify its export markets and expand ties beyond its traditional partners.
Weaponising the Strait of Hormuz is an act of economic terrorism with global impact far beyond energy markets, asserted Dr. Sultan bin Ahmed Al Jaber, Minister of Industry and Advanced Technology, while addressing CERAWeek in Houston, Texas.