Victor Pinchuk, a Ukrainian steel magnate, has sought closer ties for Ukraine to the West. He donated $150,000 to the Trump Foundation in 2015 in exchange for a brief appearance by Mr. Trump via video at a conference in Ukraine.

WASHINGTON — The special counsel is investigating a payment made to President Trump’s foundation by a Ukrainian steel magnate for a talk during the campaign, according to three people briefed on the matter, as part of a broader examination of streams of foreign money to Mr. Trump and his associates in the years leading up to the election.

Investigators subpoenaed the Trump Organization this year for an array of records about business with foreign nationals. In response, the company handed over documents about a $150,000 donation that the Ukrainian billionaire, Victor Pinchuk, made in September 2015 to the Donald J. Trump Foundation in exchange for a 20-minute appearance by Mr. Trump that month through a video link to a conference in Kiev.

Michael D. Cohen, the president’s personal lawyer whose office and hotel room were raided on Monday in an apparently unrelated case, solicited the donation. The contribution from Mr. Pinchuk, who has sought closer ties for Ukraine to the West, was the largest the foundation received in 2015 from anyone besides Mr. Trump himself.

The subpoena is among signs in recent months that the special counsel, Robert S. Mueller III, is interested in interactions that Mr. Trump or his associates had with countries beyond Russia, though it is not clear what other payments he is scrutinizing.

Mr. Mueller also ordered the Trump Organization to turn over documents, emails and other communications about several Russians, including some whose names have not been publicly tied to Mr. Trump, according to the three people, who would not be named discussing the ongoing investigation. The identities of the Russians were unclear.

The payment from Mr. Pinchuk “is curious because it comes during a campaign and is from a foreigner and looks like an effort to buy influence,” said Marcus S. Owens, a former head of the Internal Revenue Service division that oversees tax-exempt organizations. He called the donation “an unusual amount of money for such a short speech.”

Mr. Cohen did not respond to a request for comment. Jay Sekulow, a lawyer for the president, did not return several messages seeking comment, nor did a lawyer for the Trump Organization. When The New York Times revealed the existence of the subpoena in March, Mr. Trump’s associates played it down as a routine court order to ensure the Trump Organization had handed over all the documents Mr. Mueller had demanded.

Mr. Trump assailed the special counsel investigation on Monday as a “witch hunt,” reaching for a favored insult in response to the seizure of Mr. Cohen’s records. He complained that he had cooperated with the inquiry and viewed the warrant for the raid, obtained by federal prosecutors in Manhattan after a referral from Mr. Mueller, as an extreme step.

“It’s a disgraceful situation,” he told reporters at the White House. “It’s a total witch hunt. I’ve been saying it for a long time. I’ve wanted to keep it down. I’ve given over a million pages in documents to the special counsel.”

Mr. Mueller has also examined a deal…