WASHINGTON—A longtime Republican activist who led an operation hoping to obtain Hillary Clinton emails from hackers listed senior members of the Trump campaign, including some who now serve as top aides in the White House, in a recruitment document for his effort.

The activist, Peter W. Smith, named the officials in a section of the document marked “Trump Campaign.” The document was dated Sept. 7, 2016. That was around the time Mr. Smith said he started his search for 33,000 emails Mrs. Clinton deleted from the private server she used for official business while secretary of state. She said the deleted emails concerned personal matters. She turned over tens of thousands of other emails to the State Department.

As reported Thursday by The Wall Street Journal, Mr. Smith and people he recruited to his effort theorized the deleted emails might have been stolen by hackers and might contain matters that were politically damaging. He and his associates said they were in touch with several groups of hackers, including two from Russia they suspected were tied to the Moscow government, in a bid to find any stolen emails and potentially hurt Mrs. Clinton’s prospects.

Mr. Smith’s purpose in listing the officials isn’t clear. There is no indication in the document that he sought or received any coordination from the campaign officials or the campaign in general.

Mr. Smith died in mid-May at age 81, about 10 days after he spoke to the Journal. He said he operated independently of the Trump campaign.