The US Justice Department has written to Elon Musk’s super PAC warning the billionaire Tesla CEO’s $US1 million ($1.5 million) giveaways may violate federal law.

The department’s public integrity section, which investigates potential election-related law violations, was behind the letter, according to CNN.

The Justice Department and Musk’s America PAC did not immediately respond to a request for comment.

In the US, political action committees are tax-exempt organisations that pool donations and pass them on to particular candidates.

South African-born Musk has thrown his support behind Republican presidential candidate Donald Trump ahead of the November 5 election.

On Saturday (US time), he told a crowd in Pennsylvania that he would give away $1 million each day until the election to someone who had signed his online petition supporting the US Constitution.

He handed $1 million cheques to two people at the weekend – one to a man called John Dreher in Harrisburg on Saturday and another to a woman called Kristine Fishell in Pittsburg on Sunday.

“Thank you so much. I truly believe everything you’re doing. You don’t need to be doing it,” Fishell said.

“Your wealth and responsibility you are using to save speech, and we just all appreciate it. Thank you so much.”

Musk’s promise of seven-figure prizes for registered voters raised immediate concerns among election law experts and some state officials.

His petition is in support of First and Second Amendment freedoms.

Only registered voters in “Arizona, Michigan, Georgia, Nevada, North Carolina, Pennsylvania, or Wisconsin” are able to sign it – while US federal law bars paying people to register to vote.

Musk, ranked by Forbes as the world’s richest person, has so far given at least $US75 million ($113 million) to America PAC, according to federal disclosures.

That level of donation has made the group a crucial part of Trump’s bid to regain the White House.

-with AAP