At least $50 million allegedly diverted from a state investment fund in Malaysia was spent on luxury properties in New York and Los Angeles by the stepson of the Malaysian prime minister, according to documents reviewed by The Wall Street Journal and people familiar with the matter.

Riza Aziz, a film producer and stepson of Malaysian leader Najib Razak, used money that originated from the 1Malaysia Development Bhd. fund to acquire a 7,700-square-foot, $33.5 million duplex in the Park Laurel condominium tower overlooking New York’s Central Park, the documents and people said.

Mr. Aziz also used money originating from 1MDB to buy an 11,000-square-foot walled mansion in Beverly Hills with a 120-foot-long pool for more than $17.5 million, the documents and people said.

The financing of those acquisitions is under investigation by the Federal Bureau of Investigation, which is conducting a wide-ranging inquiry into alleged misappropriation of billions of dollars from 1MDB, according to people familiar with the probe. 1MDB was set up in 2009 to benefit the Malaysian people.

Investigators believe that money used to buy the two properties was part of at least $238 million—more than the Journal previously reported—that was transferred to an offshore company wholly owned by Mr. Aziz, Red Granite Capital, by a firm which investigators believe played a central role in the alleged multibillion-dollar fraud. The Journal previously reported that Mr. Aziz’s film company received $155 million in loans originating with 1MDB, much of which went to finance the 2013 movie “The Wolf of Wall Street.”