India, April 30 -- The Supreme Court on Monday rejected an appeal from Elon Musk over a settlement with securities regulators that requires him to get approval in advance of some social media posts that relate to Tesla, the electric vehicle company he leads.

The justices did not comment in leaving in place lower-court rulings against Musk, who complained that the requirement amounts to "prior restraint" on his speech in violation of the First Amendment.

The case stems from messages Musk posted on Twitter in 2018 in which he claimed he had secured funding to take Tesla private. The tweets caused the company's share price to jump and led to a temporary halt in trading.

The settlement with the Securities and Exchange Commission included a...