"We must demand that the extremely wealthy pay their fair share," Sanders said in a tweet.
Musk responded to the 80-year-old Vermont Senator by saying: "I keep forgetting that you're still alive" and later raised the possibility of selling more Tesla shares, which would require him to pay taxes. Want me to sell more stock, Bernie?"
Musk, owner of Tesla as well as SpaceX and has a personal worth estimated at around $271 billion, making him by some counts the richest person ever.
Musk and Sanders have sparred previously, with the Senator telling the tech billionaire in March to "focus on Earth" instead of aiming his vast wealth at interplanetary travel.
As the chair of the Senate's budget committee, Sanders has proposed an annual tax on the top 0.1 per cent of US households, which he claims will raise about $4.35 trillion over the next decade.
Democrats have put forward a proposal to tax billionaires as a way to fund President Joe Biden's social spending plans.
Musk sold roughly $6.9 billion worth of Tesla stocks last week in one of the largest-ever stock disposals by a chief executive over a several-day period.
According to a regulatory filing, the Tesla CEO reported selling 1.2 million shares on November 12, worth more than $1.2 billion, reports The Wall Street Journal.
Those sales came on top of more than $5.6 billion worth of stock sales last week.
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