Elon Musk is facing questions about how much attention he is paying to his businesses as he advises President Trump on the direction of the federal government.

The questions have mounted as Mr. Musk’s business empire — which includes the electric car maker Tesla, the social media site X and the rocket maker SpaceX — has run into challenges.

On Monday, users of X reported widespread outages. The same day, Tesla’s stock fell more than 15 percent amid concerns that include declining electric vehicle sales and politically driven protests against the manufacturer. And last week, a SpaceX rocket exploded in Florida during launch, showering some places with debris.

Mr. Musk on Monday quickly blamed the X issues on a cyberattack stemming from Ukraine, without providing evidence. He posted on X that Democratic donors were responsible for seeding protests against Tesla, again without evidence. In response to the SpaceX explosion, he said on X: “Rockets are hard.”

Questions about Mr. Musk’s continuing oversight of his companies are coming to a head as he spends more time in Washington on a major cost-cutting initiative known as the Department of Government Efficiency, trimming thousands of government jobs and contracts. But even there, he is facing questions about his role after a contentious cabinet meeting last week in which Mr. Trump limited Mr. Musk’s power to advising the departments.

The effects of Mr. Musk’s government involvement are particularly prominent at Tesla. The company, where Mr. Musk is chief executive, has faced protests and violence at some of its dealerships, including shots fired last week at a dealership in Oregon. In Boston, someone set fire to Tesla charging stations, and protesters were arrested at a nonviolent rally at a Tesla dealership in Lower Manhattan.

Also last week, a report found Tesla car sales in Germany, Europe’s largest market for electric vehicles, dived 76 percent in February compared with a year earlier, sounding alarm bells for the entire European market. Monday’s stock decline — more than 50 percent lower than a mid-December peak — was the biggest for Tesla stock since 2020.

X, which Mr. Musk purchased in 2022, experienced intermittent outages on Monday, mostly on its app, according to Downdetector, which tracks reports of problems from users on websites.

The first outages were reported before 6 a.m. Eastern time, after which the site and app seemed to resume functioning. But about 10 a.m. more problems arose, and there were 41,000 reports of outages on X, according to Downdetector. Shortly after 11 a.m., a third spike of reported outages emerged, and the site remained down for many users.

“There was a massive cyberattack to try to bring down the X system with IP addresses originating in the Ukraine area,” Mr. Musk said during a Monday interview with Fox’s Larry Kudlow.

But in a post on the messaging app Telegram, a hacking activist group known as Dark Storm took credit on Monday for causing the outage. Cyber criminals sometimes take steps to route their attacks through false IP addresses in order to conceal their identities, making it difficult to know for certain from which country an attack originated.

A live audio conversation on X between Mr. Musk and President Trump last year was disrupted by technical problems, which Mr. Musk also blamed on cyberattacks without providing evidence.

Representatives for X did not immediately respond to questions about what had happened Monday or whether the social media platform had returned to full operability. Mr. Musk did not immediately respond to a request for comment.

The Cybersecurity and Infrastructure Security Agency, which is part of the Department of Homeland Security, referred a request on Monday for comment on the matter to X.