The Justice Department sent a letter to the super PAC founded by Elon Musk this week warning that awarding $1 million to registered voters who signed a petition might violate federal laws against paying voters, according to two people with knowledge of the situation.

Similar warning letters from the department’s public integrity unit have been sent to businesses and organizations that tied promotions to voting and are intended to suggest that continuing such an activity could result in a criminal investigation.

The letters typically do not outline the department’s next steps and are intended to force the recipient to make changes to conform with the law.

A Justice Department spokesman declined to comment. Mr. Musk, the super PAC and its lawyer did not offer a comment on Tuesday or Wednesday. The news was first reported by the 24Sight newsletter.

It is illegal to pay people to register to vote. The idea for Mr. Musk’s petition in support of the First and Second Amendments was novel, coming in part from one of Mr. Musk’s longtime executives who was advising the super PAC, called America PAC. But some campaign-finance lawyers and Democrats said they believed it overstepped by inducing people to register with the sweepstakes.

Three voters in Pennsylvania and one in North Carolina have been awarded $1 million checks, and Mr. Musk has promised to award one voter $1 million every day through Election Day as part of his efforts on behalf of former President Donald J. Trump’s presidential campaign.

In 2010, the Justice Department warned Vince McMahon, then the owner of the World Wrestling Entertainment, when he offered free WWE clothing to voters, writing that it would be “a federal offense to pay or offer to pay an individual a thing of value for voting.”

Mr. Musk’s defenders had said the move was not illegal because it merely paid people who signed a petition — and did not specifically award people for registering to vote. But Mr. Musk has said that one of his goals in Pennsylvania was to register voters, and the petition was open only to registered voters in battleground states. Mr. Musk’s group recently began referring to its winners as “spokespeople” for the super PAC.

The super PAC initially offered $47 to people who referred signers to the petition. It has said that it collected over 1 million signatures for the petition in battleground states, meeting the group’s stated goal.