FERRARA, Italy — What was once a conspiracy theory on America’s far-right fringe has developed into a furtive international investigation by the Trump administration and a political headache, and opportunity, for Italy’s bickering leaders.

Former Prime Minister Matteo Renzi said on Friday that he was suing a 2016 campaign aide to President Trump for slander because the aide told an Italian right-wing newspaper that Mr. Renzi, while in office, had sought under the orders of President Barack Obama to derail Mr. Trump’s candidacy by planting a spy in a small Roman university.

Those accusations, previously considered the stuff of conspiracies, gained oxygen this month when it was revealed that Attorney General William P. Barr had twice visited Rome to look into them. The Italian news media has reported that Italy’s prime minister, Giuseppe Conte, whom Mr. Trump has called his “friend,” arranged for Mr. Barr to have secret meetings with the leaders of Italy’s intelligence agencies in August and September.

This has clearly delighted George Papadopoulos, the onetime Trump campaign adviser who pleaded guilty in October 2017 to lying to the F.B.I. about contacts with people who claimed to be connected to the Kremlin, and who has written a book on the subject.