Shares of the auto maker rose about five per cent in pre-market trading, rebounding from the biggest one-day fall in four-and-a half years.
Musk's role in sweeping cuts to the federal workforce at the behest of Trump has led to protests in the US against Tesla.
About 350 demonstrators protested outside a Tesla electric vehicle dealership in Portland, Oregon, last week, while nine people were arrested during a raucous demonstration outside a New York City Tesla dealership earlier in March.
Musk is spearheading the Trump administration's so-called Department of Government Efficiency, or DOGE.
In a post on his Truth Social platform, Trump defended Musk, saying he was "putting it on the line" to help the country and was doing a "fantastic" job.
"I'm going to buy a brand new Tesla tomorrow morning as a show of confidence and support for Elon Musk, a truly great American," Trump said.
Musk thanked the president for his support on his own social media platform X.
Trump in January took aim at electric vehicles, revoking a 2021 executive order signed by his predecessor Joe Biden that sought to ensure half of all new vehicles sold in the US by 2030 were electric.
Tesla's market capitalisation has more than halved since hitting an all-time high of $1.5 trillion on December 17, erasing most of the gains the stock made after Musk-backed Trump won US election in November.
The stock's decline since December stems from falling vehicle sales and profits, protests against Musk's political activity and investor worries that politics was distracting the world's richest man from tending to his cash cow.
