Manhattan state prosecutors have subpoenaed the Trump Organization for documents related to a hush payment to a former adult-film star during the 2016 election, according to a person familiar with the matter, the latest investigation to examine the company’s involvement in the payment.

The subpoena sought documents from the company, owned by President Trump and managed by his sons, related to the $130,000 paymentMichael Cohen, a former Trump lawyer, made to Stephanie Clifford in October 2016. Ms. Clifford, known professionally as Stormy Daniels, had alleged an affair with Mr. Trump, which he has denied.

The Manhattan district attorney’s office has also subpoenaed American Media Inc., the publisher of the National Enquirer, people familiar with the matter said. American Media made another payment, also arranged by Mr. Cohen, to a former Playboy model who alleged an affair with Mr. Trump. The president has also denied that affair.

Mr. Cohen in August 2018 pleaded guilty to federal charges including two campaign-finance violations related to the hush payments, which he has said he arranged at Mr. Trump’s direction. Mr. Trump has denied wrongdoing. Mr. Cohen began a three-year prison sentence in May.

Marc Mukasey, an attorney for the Trump Organization, called the investigation a “political hit job.” In a statement, he said, “It’s just harassment of the president, his family, and his business, using subpoenas and leaks as weapons. We will respond as appropriate.”