A separate White House official had said earlier that Trump and Musk were going to talk to each other on Friday.
"I'm not even thinking about Elon. He's got a problem, the poor guy's got a problem," Trump told CNN on Friday morning.
Trump, the world's most powerful leader, and Musk, the world's richest man, battled openly on Thursday in an extraordinary day of hostilities - largely over social media - that marked a stark end to a close alliance.
Shares in Musk's Tesla rose 4.5 per cent when markets opened on Friday. In Thursday's session, the stock dived 14 per cent and lost about $150 billion in value, the largest single-day decline in the electric vehicle maker's history.
Musk bankrolled a large part of Trump's presidential campaign and was then brought to the White House to head up a controversial effort to downsize the federal workforce and slash spending.
The falling-out began brewing days ago when Musk, who left his role as head of the Department of Government Efficiency a week ago, denounced Trump's tax-cut and spending bill. The feud is complicating efforts to pass the bill, which is the president's main demand of the Republican-controlled Congress.
Musk has denounced the package, which contains most of Trump's domestic priorities, as a "disgusting abomination" that would add too much to the nation's $36.2 trillion in debt.
The package narrowly passed the House of Representatives last month and is now before the Senate, where Republicans say they will make further changes. Nonpartisan analysts say it would add $2.4 trillion in debt over 10 years.
House Speaker Mike Johnson said he has been in touch with Musk.
"I don't argue with him about how to build rockets and I wish he wouldn't argue with me about how to craft legislation and pass it," he said on CNBC.
Trump had initially stayed quiet while Musk campaigned to torpedo the bill, but broke his silence on Thursday, telling reporters he was "very disappointed" in Musk.
"Look, Elon and I had a great relationship. I don't know if we will anymore," he said.
The pair then traded barbs on their social media platforms: Trump's Truth Social and Musk's X.
"Without me, Trump would have lost the election," wrote Musk, who spent nearly $300 million backing Trump and other Republicans in last year's election.
Musk also asserted that Trump's signature import tariffs would push the US into a recession and responded "Yes" to a post on X saying Trump should be impeached. That would be highly unlikely given Trump's Republicans hold majorities in both chambers of Congress.
Trump, for his part, suggested he would terminate government contracts with Musk's businesses, which include rocket company SpaceX and its satellite unit Starlink.
Musk, whose space business plays a critical role in the US government's space program, responded that he would begin decommissioning SpaceX's Dragon spacecraft, which is the only US spacecraft capable of sending astronauts to the International Space Station. He backed off the threat later in the day.
Musk had already said he planned to curtail his political spending, and on Tuesday he called for "all politicians who betrayed the American people" to be fired next year.
His involvement with the Trump administration has provoked widespread protests at Tesla sites, driving down sales while investors fretted that Musk's attention was too divided.Â
with AP
