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Law enforcement officials reportedly investigated whether US president Donald Trump was secretly working for Russia.
The New York Times reported the inquiry was launched amid concerns about Mr Trump's behaviour after he sacked former FBI director James Comey.
Counterintelligence investigators were said to have evaluated whether Mr Trump was a potential threat to national security, while also seeking to determine whether he was deliberately working for Russia - or had unintentionally been influenced by Moscow.
Mr Trump launched an attack on the FBI on Saturday, tweeting: "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!"
The Times reported FBI agents and top officials became suspicious of Mr Trump's ties to Russia during the 2016 presidential election campaign.
An investigation wasn't launched, but the president's behaviour in the days around Mr Comey's sacking in May 2017 - specifically two instances in which he seemed to tie Mr Comey's ousting to the Russia investigation - reportedly helped trigger the probe. © Provided by Independent Digital News & Media LimitedJames Comey was fired in May 2017 (AP)
It was part of an overall investigation looking into Russian election interference, and whether Mr Trump's campaign coordinated with the Russians. The Times said it's unclear whether Mr Mueller is still pursuing the counterintelligence angle.
Mr Trump has repeatedly and vociferously denied collusion with Russia.
Additional reporting by Associated Press.