(Reuters) -Elon Musk, the billionaire CEO of Tesla, publicly endorsed Donald Trump for the first time in the U.S. presidential race, calling the Republican former president "tough."

Musk tweeted the endorsement with a video of Trump pumping his fist after multiple shots rang out at Trump's rally in Pennsylvania, as video showed the Republican candidate grimacing and raising a hand to his right ear.

"I fully endorse President Trump and hope for his rapid recovery," Musk posted on his social media platform X.

"The martyr lived," he wrote in a later post.

The posts cement Musk's shift towards right-wing politics and hand Trump a high-profile backer in his quest to return to the White House in the Nov. 5 election.

Musk later posted a photograph of Trump at the event, followed by: "Last time America had a candidate this tough was Theodore Roosevelt."

Musk and representatives from X did not immediately respond to requests for comment.

Musk, who has been ramping up criticism of U.S. President Joe Biden, has donated to a political group working to elect Trump, Bloomberg reported on Friday, citing sources.

The South African-born businessman's sway stands to benefit Trump, since Musk has one of the largest footprints on X with 189.5 million followers, meaning his posts can instantaneously spread widely.

Musk has said he previously voted for Democratic presidential candidates Hillary Clinton as well as Biden.

However, in the last few years, Musk has espoused right-wing views, becoming a fierce critic of diversity initiatives, Biden's immigration policies and complaining that Democrats had given a "very cold shoulder" to Tesla and rocket company SpaceX.

Since his acquisition of the social media platform formerly known as Twitter, critics and social media researchers have noted spikes in hateful content, in part due to Musk's promises to reduce the company's content moderation policies.

In March, Trump, who is expected to be formally nominated next week as the Republican Party's candidate for the Nov. 5 election, met with Musk and other wealthy donors.

In response to reports of the meeting, Musk posted on X: "Just to be super clear, I am not donating money to either candidate for US President." In May, he also denied media reports that there had been talks over a potential advisory role for him in any Trump presidency.