In a written exchange with the Washington Post, Page confirmed playing a role in the case but declined to discuss details.
"Given the very light masking in the original document from January 2015, you can draw your own conclusions," Page wrote.
According to the court records, the FBI interviewed Page as part of the case against three Russian men identified as agents of the Russian overseas intelligence agency, the SVR.
One of them, Buryakov, was operating undercover as an executive in the New York office of a Russian development bank, VneshEconomBank.
The case resurfaced in news accounts last week when Trump's adviser and son-in-law, Jared Kushner, acknowledged he had met the head of the same bank in December.
The complaint includes transcripts from 2013 of wiretapped conversations among the Russians discussing their efforts to recruit Male 1, identified as a New York energy trader whom the Russians described as willing to talk.
In his statement, Page compared the revelation of his role to "the politically-motivated unmasking standards seen in the Obama Administration which have recently been exposed".
He said the information was released as "retribution for my public positions of dissent" against the Obama Administration policy towards Russia.
The information about his role in the case "amplified the reputational damage against me" that has occurred through 2016, Page said.
After he was named by Trump, news stories discussed his travel to Russia and his frequent criticism of US policy towards Russia under Obama.
According to the 2015 complaint filed in federal court in the Southern District of New York, Page met a Russian agent, Victor Podobnyy, in January 2013 at an energy conference in New York.
It says that from January to June of that year, Page as Male 1 "provided documents to [Podobnyy] about the energy business". At the time the Russians were seeking information on US sanctions and on energy development.
Although Page communicated with the Russian agents in 2013, he said the information he provided was innocuous.
"As I explained to federal authorities prior to the January 2015 filing of this case, I shared basic immaterial information and publicly available research documents" with the spy who was serving then as a junior attaché at the Permanent Mission of the Russian Federation to the United Nations.
"In doing so, I provided him nothing more than a few samples from the far more detailed lectures I was preparing at the time for the students in my spring 2013 semester Energy and the World: Politics, Markets and Technology course which I taught on Saturdays at New York University."
During an interview with the Washington Post editorial page in March 2016, Trump identified Page, once a Merrill Lynch investment banker in Moscow, as a foreign policy adviser to his campaign.
But in January, after Page's name came up in news stories about Trump Administration ties to Russia, Trump spokesman Sean Spicer declared that "Carter Page is an individual the President-elect does not know".
Page, a longtime energy executive, is a graduate of the US Naval Academy who rose through the ranks at Merrill Lynch before founding his current firm, Global Energy Capital.
He previously was a fellow at the Council on Foreign Relations, where he focused on the Caspian Sea region and the economic development in former Soviet states. He is also a fellow at the Centre for National Policy in Washington and has a PhD from the University of London.
He made a speech in Moscow in July 2016 that included some criticism of US policy.
The White House has energetically rejected the idea that Trump or his allies coordinated with Russia during the election. The President has said investigators and the public should focus instead on leaking of information and reports that he and his advisers were improperly surveilled by the Obama Administration.
"The real story turns out to be SURVEILLANCE and LEAKING! Find the leakers," Trump tweeted yesterday.
Page has said repeatedly in recent weeks that he would like to tell his story to congressional investigators looking at Russian Government efforts to influence the course of the 2016 election and the leak of information about that effort.
"I very much look forward to providing further evidence regarding last year's historic crimes committed against me and all Americans," Page said.
