Hedge-fund manager Philip Falcone was threatened with possible civil-fraud charges from the top U.S. securities regulator, the latest in a series of setbacks that have buffeted the investor since he rocketed to stardom in 2007.

Mr. Falcone and his firm, Harbinger Capital Partners LLC, received so-called Wells notices from the Securities and Exchange Commission, according to a regulatory filing Friday, an indication that charges are likely.

Among the issues the SEC has explored is whether Harbinger agreed to allow some investors, including Goldman Sachs Group Inc., to cash out of their holdings while barring other clients from withdrawing their money, according to people familiar with the matter.

The SEC, maligned in recent years for missing multibillion-dollar Ponzi schemes and failing to hold more individuals responsible for the financial crisis, has ratcheted up its policing of hedge funds, launching a bevy of investigations aimed at the industry. The Harbinger probe comes at a time when the agency has been aggressively prosecuting insider-trading cases and targeting managers who have misled investors.

Harbinger said it is “disappointed” with the issuance of the Wells notices, and if the SEC decides to bring an enforcement action, it intends to “vigorously defend against it,” according to the filing.

The threat of SEC charges is a blow for Mr. Falcone, who was catapulted to fame on Wall Street when his successful hedge-fund bets against subprime mortgages earned him billions of dollars. Investors flocked to Harbinger, helping push its assets to a peak of $26 billion in 2008.