Carter Page, a foreign policy adviser to Donald Trump's presidential campaign, said that he has "no recollection" of discussing, during a trip to Moscow last summer, a possible easing of U.S. sanctions against Russia but that "something may have come up in a conversation."
Page traveled to the Russian capital in July 2016 to give a speech at the New Economic School.
Page said he briefly said hello to one of the school's board members.
When Stephanopoulos asked whether Page suggested in any of his conversations that Trump would be open to easing sanctions on Russia, Page initially responded, "I never offered that," but then said, "I don't recall every single word."
Stephanopoulos pressed, "It sounds like, from what you're saying, it's possible you may have discussed the easing of sanctions."
"Something may have come up in a conversation," Page replied. "I have no recollection, and there's nothing specifically that I would have done that would have given people that impression."
"Someone may have brought it up," he continued. "And if it was, it was not something I was offering or that someone was asking for."
"We'll see what comes out in this FISA transcript," he said, referring to surveillance collected after the FBI obtained a secret court order last summer to monitor him under the Foreign Intelligence Surveillance Act, as reported by The Washington Post two days ago.
Law enforcement officials suspected he might be working with the Russians and presented enough evidence, the newspaper reported, to persuade a FISA Court judge to authorize electronic surveillance of his communications.
Page added, "People make up all kinds of conspiracy theories."
Asked about the FBI's ongoing investigation into alleged ties between the Trump campaign and Russia during the 2016 presidential race, Page said, "I do not talk about any ongoing investigations. I will say that, in terms of probable cause, there's been a ton of false evidence that's been out there, primarily in the public realm."
Approval of a FISA warrant, according to John Carlin, a former assistant attorney general for national security and an ABC News contributor, requires extensive evidence.
"You have to lay out a series of facts that show that there's probable cause to believe that someone is an agent of a foreign power," Carlin said, speaking in general and not about any specific case. "It's secret because it's designed for foreign agents."
Page has repeatedly denied any wrongdoing, but The Washington Post's report is the clearest indication that his ties to Russia are a key element of the FBI's inquiry. When FBI Director James Comey appeared before Congress in March, he confirmed that his office was engaged in a probe of Russia's attempts to meddle in the election on Trump's behalf but did not specify any people under investigation.
"The FBI, as part of our counterintelligence mission, is investigating the Russian government's efforts to interfere in the 2016 presidential election," Comey told lawmakers. "And that includes investigating the nature of any links between individuals associated with the Trump campaign and the Russian government and whether there was any coordination between the campaign and Russia's efforts."
The White House, the FBI and the Department of Justice have declined to comment on the Post's report.
ABC News' Jack Date, Pete Madden, Matthew Mosk, Cho Park and Brian Ross contributed to this report.