The Guardian, which first published the existence of the reports on Mr. Rhodes and Mr. Kahl, said aides to Mr. Trump hired the firm, but there is no evidence in the documents that indicate any connection to anyone in Mr. Trump’s administration. A spokesman for the company vehemently denied any connection to the president.
“Black Cube has no relation whatsoever to the Trump administration, to Trump aides, to anyone close to the administration or to the Iran nuclear deal,” said Ido Minkowski, the company’s spokesman. “Anyone who claims otherwise is misleading their readers and viewers.”
One person with knowledge of the reports suggested that the company had been hired by a commercial client with an interest in opposing the nuclear deal.
The reports appear to be aimed at undermining public support for the agreement by finding ways to discredit Mr. Rhodes and Mr. Kahl, who have been staunch advocates of the deal on social media and in television appearances. In an interview on Monday, Mr. Rhodes said he was surprised that ferocious criticism directed at him continued after he left government.
“I never imagined that upon leaving government, that not only would that information campaign continue, but that it would be supplemented by investigations into me and my family by shadowy international operations, involving foreign entities,” Mr. Rhodes said.
The deal to curtail Iran’s nuclear weapons program was signed by the United States, Iran and several European countries in 2015. Its critics, including Mr. Trump and Benjamin Netanyahu, the prime minister of Israel, have said it does nothing to curtail the danger posed by Iran and will not curtail Iran’s ability to develop nuclear weapons. The president said Monday that he will announce on Tuesday whether he will formally withdraw the United States from the deal, as he has repeatedly signaled he would.
While there is no evidence directly linking Trump officials to the preparation of the reports, several current or former members of the Trump White House have repeatedly attacked Mr. Rhodes and Mr. Kahl for their support of the Iran agreement.
Sebastian Gorka, a Trump supporter who served briefly in the White House as an adviser, has repeatedly attacked both men on social media and in conservative news outlets, accusing Mr. Rhodes and Mr. Kahl of working to undermine Mr. Trump and defend the Iran deal from its critics.
Current and former Trump administration officials have also targeted John Kerry, the former secretary of state who negotiated the Iran deal for the United States. Even Mr. Trump himself said in a Twitter post on Monday that recent efforts by Mr. Kerry to save the deal amounted to “possibly illegal Shadow Diplomacy.”
Unlike Mr. Kerry, Mr. Kahl and Mr. Rhodes were not part of the nuclear deal negotiating team for the United States. But even before he left the White House, Mr. Rhodes was the target of criticism for his efforts to help build support for its approval.
“Why did whoever did this conjoin Ben and me? Why the two of us?” Mr. Kahl said. “Being vocal on Twitter would make me a target. But why would it bring down the Iran deal?”
A New York Times Magazine profile of Mr. Rhodes in May 2016 described a White House “war room” in which he tried to manage news coverage of the Iran nuclear negotiations. In the article, Mr. Rhodes was quoted as saying: “We created an echo chamber. They were saying things that validated what we had given them to say.”
Critics of the Iran deal have seized on the article to insist that Mr. Rhodes — and by extension, the entire Obama administration — were secretly manipulating public opinion by misrepresenting the implications of the nuclear deal.
The report on Mr. Rhodes by Black Cube notes that “in the article, he boasts about the creation of an ‘echo chamber’ in which he told journalists what to say and they repeated it back over and over as original thoughts.”
The reports also provide a list of several Washington journalists who have had “extensive contact” with Mr. Rhodes. Among those listed under the heading “contacts to investigate” are Jeffrey Goldberg, now the editor of The Atlantic; Mark Landler, a White House correspondent for The Times who often writes about foreign policy; Andrea Mitchell, now NBC News’s chief foreign affairs correspondent; and Glenn Thrush, a Times reporter who covered the Obama White House for Politico.
On Monday, reporters asked Sarah Huckabee Sanders, the White House press secretary, whether anyone at the White House had knowledge of whether aides to Mr. Trump had hired Black Cube to dig up dirt on former Obama officials.
“I’m not aware of anything on that front,” Ms. Sanders said, adding that “if something comes up, we’ll let you guys know.”