FBI director James Comey has confirmed for the first time that the FBI is investigating alleged Russian interference in the 2016 election.
However, Mr Comey said his agency had seen no evidence to back up President Trump's claim that his phones had been tapped by the Obama administration.
He was giving evidence to the congressional intelligence committee.
Mr. Comey said that it was unusual for the F.B.I.to confirm or deny the existence of any investigations, but that in unusual circumstances when it is in the public interest, the bureau will sometimes discuss such matters.
The Trump administration said nothing had changed and there was "no evidence of Trump-Russia collusion".
Russia has always denied attempting to influence the US presidential election.
The FBI investigation would examine possible links between individuals in the Trump campaign and the Russian government and whether there was co-ordination between the Trump campaign and Russia, Mr Comey said.
The FBI would also assess whether crimes were committed, he said.
Mr Comey said the investigation was "very complex" and he could not give a timetable for its completion.
"We will follow the facts wherever they lead," he said.
Mr Comey said he had no information on unsubstantiated claims tweeted by Mr Trump this month that former President Barack Obama had ordered a wiretap on Trump Tower.
This was despite looking carefully for such evidence, he said. The Department of Justice also had no information, he said.
But White House press secretary Sean Spicer suggested the administration was not concerned, saying: "You can continue to look for something, but continuing to look for something that doesn't exist doesn't matter."
National Security Agency (NSA) chief Admiral Mike Rogers also appeared before the committee.
He said the NSA stood by an intelligence community report published in January, which said that Russian President Vladimir Putin had ordered a campaign to harm the campaign of Mr Trump's rival, Hillary Clinton.