WASHINGTON — Days after the rogue website WikiLeaks posted a trove of stolen Democratic Party emails during the 2016 presidential campaign, Donald J. Trump talked by phone with Roger J. Stone Jr., a longtime friend who claimed to have connections to WikiLeaks, then told a top aide that “more information would be coming,” the aide testified in Mr. Stone’s criminal trial on Tuesday.

The aide, Rick Gates, said he did not hear the substance of the July 31, 2016, call. Nor did he say that Mr. Trump mentioned WikiLeaks, the organization that had received tens of thousands of emails stolen by Russian operatives seeking to sabotage the campaign of his opponent, Hillary Clinton.

But the context of the exchange suggests that Mr. Stone briefed Mr. Trump on whatever he had picked up about the website’s plans. In written answers that President Trump supplied during the special counsel’s investigation of Russian influence in the campaign, he said he did not recall the specifics of any of his 21 phone calls with Mr. Stone in the six months before the election. He also said he did not recall knowing that his campaign advisers were in touch with Mr. Stone about WikiLeaks.

Mr. Gates’s testimony revealed other new details about the Trump campaign’s intense interest in how WikiLeaks might disrupt Mrs. Clinton’s campaign. Much of what he said in court was covered in the 448-page report by the special counsel, Robert S. Mueller III, but it was blacked out in the version released publicly last spring to protect grand jury secrecy or open cases, a person familiar with the report said.