Federal prosecutors overseeing the investigation into former President Donald J. Trump’s handling of classified documents have issued a subpoena for information about Mr. Trump’s business dealings in foreign countries since he took office, according to two people familiar with the matter.

It remains unclear precisely what the prosecutors were hoping to find by sending the subpoena to Mr. Trump’s company, the Trump Organization, or when it was issued. But the subpoena suggests that investigators have cast a wider net than previously understood as they scrutinize whether he broke the law in taking sensitive government materials with him upon leaving the White House and then not fully complying with demands for their return.

The subpoena — drafted by the office of the special counsel, Jack Smith — sought details on the Trump Organization’s real estate licensing and development dealings in seven countries: China, France, Turkey, Saudi Arabia, Kuwait, the United Arab Emirates and Oman, according to the people familiar with the matter. The subpoena sought the records for deals reached since 2017, when Mr. Trump was sworn in as president.

The Trump Organization swore off any foreign deals while he was in the White House, and the only such deal Mr. Trump is known to have made since then was with a Saudi-based real estate company to license its name to a housing, hotel and golf complex that will be built in Oman. He struck that deal last fall just before announcing his third presidential campaign.

The push by Mr. Smith’s prosecutors to gain insight into the former president’s foreign business was part of a subpoena — previously reported by The New York Times — that was sent to the Trump Organization and sought records related to Mr. Trump’s dealings with a Saudi-backed golf venture known as LIV Golf, which is holding tournaments at some of his golf clubs. (Mr. Trump’s arrangement with LIV Golf was reached well after he removed documents from the White House.)

Collectively, the subpoena’s demand for records related to the golf venture and other foreign ventures since 2017 suggests that Mr. Smith is exploring whether there is any connection between Mr. Trump’s deal-making abroad and the classified documents he took with him when he left office.

It is unclear what material the Trump Organization has turned over in response to the subpoena or whether Mr. Smith has obtained any separate evidence supporting that theory. But since the start of their investigation, prosecutors have sought to understand not only what sorts of materials Mr. Trump removed from the White House, but also why he might have taken them with him.

Among the government documents discovered in Mr. Trump’s possession were some related to Middle Eastern countries, according to a person familiar with Mr. Smith’s work. And when the F.B.I. executed a search warrant in August 2022 at Mar-a-Lago, Mr. Trump’s private club and residence in Florida, among the items recovered was material related to President Emmanuel Macron of France, according to court records.

A spokesman for Mr. Trump did not respond to emails seeking comment. A Trump Organization spokeswoman did not immediately respond to a request for comment.

Mr. Trump has long argued that the documents belonged to him and that he need not return them to the government. When the Justice Department subpoenaed him last year to turn over any classified documents, he initially asked his lawyers whether he had to comply with the demand, according to a person with knowledge of the discussion. They said he was obligated to do so.

Since it became public that Mr. Trump had hundreds of classified documents at his private properties, including Mar-a-Lago, in early 2022, people close to him have said that he often referred to the boxes of material that federal officials wanted back as “mine.”

This month, Mr. Trump said something similar during a televised town hall event on CNN, declaring that he knowingly took government records from the White House when he left. He further claimed that he was allowed to do so because he considered the documents to be his personal property.

“I took the documents; I’m allowed to,” Mr. Trump said during the town hall, asserting at one point that he had “the absolute right” to take control of government records under the Presidential Records Act. That law, enacted in 1978 after the Watergate scandal, gave control of presidential records to the government itself — not to individual presidents.

Mr. Trump’s comments about the records being his personal property were in line with advice he was said to have received from Tom Fitton, the head of the conservative group Judicial Watch, who has given testimony to prosecutors investigating the case, according to people familiar with their conversations.

While establishing a motive for why Mr. Trump kept hold of certain documents could be helpful to Mr. Smith, it would not necessarily be required in proving that Mr. Trump willfully maintained possession of national defense secrets or that he obstructed the government’s repeated efforts to get the materials back. Those two potential crimes have long been at the heart of the government’s documents investigation.

Mr. Smith is also examining Mr. Trump’s efforts to cling to power after he lost the November 2020 election to President Biden, an inquiry that includes what role he may have played in unleashing the violence that erupted at the Capitol on Jan. 6, 2021.

A third track of Mr. Smith’s investigation is focused on Mr. Trump’s efforts to leverage claims of investigating election fraud to raise money. Mr. Trump raised tens of millions of dollars in small increments from donors as he aired allegations about election fraud that were eventually debunked.

Mr. Smith’s team is still bringing witnesses to the grand jury in connection with that matter. One witness this week is William Russell, an aide to Mr. Trump who worked for him in the White House and who was paid by Mr. Trump’s political action committee, Save America, where much of the money raised went.

Mr. Trump was recently indicted in Manhattan, where prosecutors accused him of covering up a sex scandal during the 2016 election, and is under investigation by a prosecutor in Georgia over his effort to overturn the election results there.