US President Donald Trump says it “was very nice” of Elon Musk to post a message about regretting some of his criticisms, in the latest sign of a tentative reconciliation following their royal bust-up.

Trump said on Saturday his relationship with the tech billionaire was over after incendiary exchanges on on social media, with the Tesla and SpaceX CEO describing the President’s sweeping tax and spending bill as a “disgusting abomination”.

Musk has since deleted some posts critical of Trump, including one signalling support for impeaching the President and another linking him with disgraced financier Jeffrey Epstein.

CNN reports it has been told by two sources that Musk called Trump on Monday night local time, in an exchange lasting just moments.

“I regret some of my posts about President Donald Trump last week. They went too far,” Musk wrote in a post on his social media platform X on Wednesday, without saying which specific posts he was referring to.

Sources close to the world’s richest man say his anger has started to subside and that he may want to repair the relationship.

Company and market analysts suggested Musk’s tone could reflect a desire to protect his businesses.

“I thought it was very nice that he did that,” Trump told The New York Post after Musk’s comments.

Tesla shares rose 1.7 per cent.

“The conciliatory tone from Musk recently might indicate his desire to protect his businesses in the light of the position he has found himself in,” said Mamta Valechha, consumer discretionary analyst at Tesla investor Quilter Cheviot.

Tesla shareholder Matthew Britzman, an analyst at Hargreaves Lansdown, said Musk and Trump appeared to have de-escalated the situation.

“It still feels unlikely that we’ll see these two giant personalities so closely intertwined again but it’s in neither’s best interest to let the drama continue,” he said.

Shawn Campbell, adviser and investor at Camelthorn Investments, said the relationship between Musk and Trump could be restored but also said it was unlikely it would return to where it once was.

“The stakes between the richest man in the world and leader of the most powerful nation in the world are just so big, with billions of dollars of government contracts at stake, not to mention the power to investigate and regulate and tax,” said Campbell, who personally holds Tesla shares.

Musk bankrolled a large part of Trump’s 2024 presidential campaign, spending nearly $US300 million ($A459 million) in last year’s US elections and taking credit for Republicans retaining a majority of seats in the House and retaking a majority in the Senate.

Trump then named him to head an effort to downsize the federal workforce and slash spending.

Musk left the role late last month after criticising Trump’s marquee tax bill, calling it too expensive and a measure that would undermine his work at the Department of Government Efficiency.

On Monday, Trump said he would have no problem if Musk called and that he had no plans to discontinue the Starlink satellite internet provided to the White House by Musk’s SpaceX but might move his Tesla off-site.

“We had a good relationship, and I just wish him well,” Trump said.

Musk responded with a heart emoji to a video on X showing Trump’s remarks.

Tesla shares have recouped all the losses suffered during the public feuding between Trump and Musk last Thursday, when more than $US150 billion was wiped off the company’s market value.

-with AAP