Trump said on Saturday his relationship with Musk was over after they exchanged insults 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 sources close to the world's richest man say his anger has started to subside and he may want to repair the relationship.
"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 talking about.
Tesla shares in Frankfurt rose 2.7 per cent after Musk's post.
Musk bankrolled a large part of Trump's 2024 presidential campaign, spending nearly $US300 million ($A460 million) in 2024'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 in late May 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.
Declaring their relationship over on Saturday, Trump said there would be "serious consequences" if Musk decided to fund US Democrats running against Republicans who vote for the tax and spending bill. Trump also said he had no intention of repairing ties with Musk.
On Monday, Trump said he would not have a 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.
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