The New York Times, citing sources, reported Friday that after Trump fired FBI Director James Comey in 2017, law enforcement officials launched an investigation about "whether he had been working on behalf of Russia against American interests."
The probe reportedly was sparked by concerns that Trump fired Comey in May 2017 to quash the FBI's ongoing investigation into Russian interference in the 2016 presidential election.
A day after the Times report, Trump had a phone interview with Fox News host Jeanine Pirro, a friend of his, on her televised show.
During that interview, Trump avoided answering Pirro when she asked whether he currently is working for Russia or had ever done so.
"I think it's the most insulting thing I've ever been asked," Trump said.
"I think it's the most insulting article I've ever had written, and if you read the article you'll see that they found absolutely nothing."
The Washington Post reported Sunday that Trump, in an effort to conceal details of his talks with Putin, took possession of the notes of his own interpreter at least once. He also alleged told her not to talk with other officials in the Trump administration about what had been discussed.
The Post, citing U.S. officials, said there is no detailed record, classified or otherwise, of Trump's "face-to-face interactions with the Russian leader at five locations over the past two years."
"It's a lot of fake news," Trump said Monday about the report.
"That was a very good meeting," Trump said, referring to his talk with Putin. "I have those meetings, one-on-one, with all leaders, including the president of China and the prime minister of Japan."
The president's comments come as special counsel Robert Mueller is expected to soon submit a report on his investigation of Russia's interference in the election, whether members of the Trump campaign colluded with Moscow and whether Trump obstructed justice.
The question of whether Trump obstructed justice is seen by many to be related to the president's rationale for firing Comey.
Trump's lawyers have said he had every right to terminate the FBI director.
Trump told NBC News in 2017 that he fired Comey in part because he realized, "This Russia thing with Trump and Russia is a made up story."
Trump said Monday he had done the United States "a great service" by firing Comey.
Comey has said that three months before he was terminated, Trump asked him to shut an FBI probe into Trump's first national security adviser, Michael Flynn.
The retired Army lieutenant general, who was fired by Trump after less than a month in office, later pleaded guilty to lying to the FBI about the nature of his discussions with Russia's ambassador to the United States on the heels of the 2016 election.
"He was a bad cop and he was a dirty cop and he lied, he really lied," Trump said of Comey on Monday.
On Saturday, Trump tweeted: "Wow, just learned in the Failing New York Times that the corrupt former leaders of the FBI, almost all fired or forced to leave the agency for some very bad reasons, opened up an investigation on me, for no reason & with no proof, after I fired Lyin' James Comey, a total sleaze!"
He continued that tirade on Twitter as the day continued.
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