President Trump assailed Elon Musk on Sunday night, describing him as “off the rails” after Mr. Musk said he was creating a new political party amid an ongoing rift with the president.

“I am saddened to watch Elon Musk go completely ‘off the rails,’ essentially becoming a TRAIN WRECK over the past five weeks,” Mr. Trump wrote on Truth Social on Sunday evening. “He even wants to start a Third Political Party, despite the fact that they have never succeeded in the United States.”

Mr. Musk’s effort to create a new political party, called the America Party, is the latest rupture in his relationship with Mr. Trump. Mr. Musk, the world’s wealthiest man, spent hundreds of millions of dollars to support Mr. Trump’s presidential campaign, and then Mr. Trump rewarded him with a wide-ranging position overseeing drastic cuts to government staffing and contracts.

Their close bond crumbled in a public spectacle last month, as Mr. Trump pushed his sprawling domestic policy bill through Congress. Mr. Musk panned the legislation, which is projected to add trillions to the federal debt, as a “disgusting abomination.” He has said he would support primary challengers against any Republican who voted for the legislation, which passed with almost unanimous Republican support, but he has given few details about his new political party.

“Backing a candidate for president is not out of the question, but the focus for the next 12 months is on the House and the Senate,” Mr. Musk wrote on X on Sunday.

Mr. Trump has also threatened to cut billions of dollars in federal contracts and tax subsidies for Mr. Musk’s companies.