WASHINGTON – Former acting FBI Director Andrew McCabe hinted at an "inappropriate relationship" between President Donald Trump and Russia during a wide-ranging interview on CBS' "60 Minutes" that has already sparked calls for a congressional investigation.

Speaking to "60 Minutes" correspondent Scott Pelley, McCabe said the FBI had reasonable cause to open a counterintelligence investigation into Trump's connection with the Russian government, a potential national security threat, following the firing of then-FBI Director James Comey in May 2017.

He also said Deputy Attorney General Rod Rosenstein was "not joking" when he offered to wear a wire into the White House to "collect evidence" into Trump's motivation for firing Comey.

"And the idea is, if the president committed obstruction of justice, fired the director of the FBI to negatively impact or to shut down our investigation of Russia's malign activity and possibly in support of his campaign, as a counterintelligence investigator, you have to ask yourself, 'Why would a president of the United States do that?'" McCabe said on "60 Minutes."

"So all those same sorts of facts cause us to wonder if there is an inappropriate relationship, a connection between this president and our most fearsome enemy, the government of Russia?"

Asked by Pelley if Trump is "in league with the Russians," McCabe said, "I'm saying that the FBI had reason to investigate that. Right – to investigate the existence of an investigation doesn't mean someone is guilty. I would say, Scott, if we failed to open an investigation under those circumstances, we wouldn't be doing our jobs."

Prior to the airing of McCabe's interview, Sen. Lindsey Graham, R-South Carolina, said Sunday he planned to conduct a Senate investigation into what he characterized as "an attempted bureaucratic coup."

"We're going to find out what happened here and the only way I know to find out is to call the people in under oath and find out, through questioning, who's telling the truth because the underlying accusation is beyond stunning," Graham said on CBS' "Face the Nation."

Graham, the chairman of the Senate Judiciary Committee, added that he would subpoena McCabe and Rosenstein if they did not agree to testify voluntarily.

Via Twitter, Trump responded Thursday to the news of McCabe's interview by calling him a "disgrace to the FBI and to our Country" who was trying to pretend to be a "poor little Angel." He also repeated many of his past criticisms of McCabe, who he says helped start the "Russia hoax" and was biased in favor of Hillary Clinton.

During the "60 Minutes" interview, McCabe said Rosenstein resisted Trump's insistence of referencing Russia in a memo to justify Comey's firing — "And the president responded, 'I understand that, I am asking you to put Russia in the memo anyway,'" he said — and later raised the idea of wearing a wire to the White House.

"He said, “I never get searched when I go into the White House. I could easily wear a recording device. They wouldn’t know it was there,” McCabe said. "Now, he was not joking. He was absolutely serious. And, in fact, he brought it up in the next meeting we had."

He added, "I never actually considered taking him up on the offer."

The Justice Department last September, responding to a New York Times report that first revealed the conversation, issued a statement from another official who was in the room and interpreted Rosenstein's offer as sarcastic.

Asked during Sunday's interview if Rosenstein supported obstruction and counterintelligence investigations against Trump, McCabe answered, "Absolutely."

McCabe was fired from the Justice Department last March by then-Attorney General Jeff Sessions for "an unauthorized disclosure to the news media and lacked candor − including under oath − on multiple occasions." In the "60 Minutes" interview, McCabe described his firing as politically motivated, telling Pelley he was authorized to release information to the media.

Graham's "coup" comment echoed criticisms from other Republicans and Trump supporters who have long claimed there is a "deep state" conspiracy of career Justice Department officials against the president. They believe that the opening of special counsel Robert Mueller's investigation into a potential conspiracy between the Trump campaign and Russians trying to sway the 2016 election is a part of that conspiracy.

"When is someone going to finally investigate the investa(g)tors?" tweeted the president's oldest son, Donald Trump Jr., on Friday. "If this isn’t an attempted coup I don’t know what is. Regardless of party if you’re not troubled by this, you’re part of the problem."

In the "60 Minutes" interview, McCabe recalled meeting with Trump after the president had just fired Comey.

"I was speaking to the man who had just run for the presidency," McCabe said. "And won the election for the presidency and who might have done so with the aid of the government of Russia, our most formidable adversary on the world stage."

"And that was something that troubled me greatly," he added.

When Pelley asked how long after Comey's firing he decided to begin an investigation into possible obstruction of justice by the president, McCabe replied, "I think the next day, I met with the team investigating the Russia cases and I asked the team to go back and conduct an assessment to determine 'Where are we with these efforts and what steps do we need to take going forward?'"

McCabe said he was "very concerned" and wanted to make sure that he had "the Russia case on absolutely solid ground, in an indelible fashion." He said wanted to make sure that if he was "removed quickly, or reassigned or fired, that the case could not be closed or vanish without a trace in the night."

His book, “The Threat: How the FBI Protects America in the Age of Terror and Trump," hit bookshelves on Tuesday.

Contributing: The Associated Press