FBI director James Comey has confirmed for the first time that the FBI is investigating alleged Russian government interference in the 2016 election.
That includes possible links between individuals in the Trump campaign and the Russian government and whether there was co-ordination between the Trump campaign and Russia, he said.
The FBI would also assess whether crimes were committed, he said.
Mr Trump has denied any collusion.
“There is no evidence of Trump-Russia collusion and there is no evidence of a Trump-Russia scandal,” a senior White House official said in a statement.
Russia has always denied attempting to influence the US presidential election.
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The FBI director was speaking at a rare open hearing of the congressional intelligence committee, which is also investigating possible links between the Trump campaign and Russia.
Mr Comey said the investigation was “very complex” and said he could not give the committee details that were not already publicly known.
He also said he could not give a timetable for its completion.
“We will follow the facts wherever they lead,” he said.
Also testifying before the committee is National Security Agency (NSA) chief Admiral Mike Rogers.
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.
‘No wiretap on Trump Tower’
Both officials also denied unsubstantiated claims tweeted by Mr Trump earlier this month that former president Barack Obama had ordered a wiretap on Trump Tower.
Mr Comey said he had no information that supported the tweets and neither did the Department of Justice.
He added that no individual – including a president – could unilaterally order someone to be put under electronic surveillance. Instead there had to be an application that was then granted by a judge.
Analysis – BBC North America reporter Anthony Zurcher
What FBI Director James Comey didn’t say during intelligence hearings today on possible Russian meddling in the 2016 US election was as important as what he did say.
Former Trump campaign manager Paul Manafort, who had ties to pro-Russian Ukrainian politicians? No comment. Long-time Trump adviser Roger Stone, who reportedly had communications with individuals who hacked the Democratic National Committee emails? No comment. Former National Security Adviser Michael Flynn, who was forced to resign after leaked evidence surfaced that he had communicated with a Russian ambassador about US sanctions? No comment.
“I don’t want to answer any questions about a US person,” Mr Comey said.
All of this is evidence that the investigation isn’t just ongoing, it’s substantive and far-reaching.
While Democrats will likely be encouraged by this, it was telling that Republicans pursued the White House line that the topic of greatest concern was the intelligence leaks that put this story in the headlines.
If Mr Trump can consolidate his party’s support, it will go a long way towards insulating the president against any fallout from this investigation.
Meanwhile, Admiral Rogers said the NSA had not asked Britain’s GCHQ intelligence agency to spy on Mr Trump – a claim that had been repeated by Mr Trump’s spokesman, Sean Spicer.
“That would be expressly against the construct of the five-eyes agreement that’s been in place for decades,” he said. The allegation “clearly frustrates a key ally of ours”, he added.
GCHQ has described the claim as “utterly ridiculous”. Under the five-eyes agreement, the US, UK, Australian, Canadian and New Zealand intelligence agencies share information and do not spy on each other.
Admiral Rogers also said that Mr Trump’s recent joke about how Mr Obama wiretapped both German Chancellor Angela Merkel and him, “complicates things” with an ally.
However, Devin Nunes, the Republican chairman of the House of Representatives Intelligence Committee, said it was still possible that other surveillance activities had been used against Mr Trump and his associates.
What are the allegations?
In January, US intelligence agencies said Kremlin-backed hackers had broken into the email accounts of senior Democrats and released embarrassing ones in order to help Mr Trump defeat Hillary Clinton.
Since then, Mr Trump has faced allegations that his campaign team had links to Russian officials.
Mr Comey told the congressional committee that Mr Putin “hated Hillary Clinton so much” that he had a strong preference for the candidate running against her.
He also said Russia’s “number one mission” was to “undermine the credibility of the entire democratic exercise of this nation”.
The Russian hacking had been “unusually loud” and it was “almost as if they wanted us to see what they were doing” – perhaps to “freak people out” about how they were undermining the election, Mr Comey said.
Mr Nunes said on Sunday that based on “everything I have up to this morning” there is “no evidence” that the Trump campaign colluded with Russia.
Former Director of National Intelligence James Clapper has also said he saw no evidence of any collusion, up until the time he left his post in January.
However, Adam Schiff, the committee’s top Democrat, said the material he had seen offers circumstantial evidence that US citizens collaborated with Russians to influence the vote.
If the Trump campaign was found to have colluded with Russia it would be “the most shocking betrayal of democracy in history”, Mr Schifff told the committee.
Which campaign members have been accused of deception?
Two senior officials in the Trump administration have been caught up in the allegations – former national security adviser Michael Flynn, and Attorney-General Jeff Sessions.
Mr Flynn was fired last month after he misled the White House about his conversations with the Russian ambassador before he was appointed national security adviser.
He allegedly discussed US sanctions with ambassador Sergei Kislyak. It is illegal for private citizens to conduct US diplomacy.
Meanwhile, Mr Sessions was accused by Democrats of lying under oath during his confirmation hearing in January.
He said he had “no communications with the Russians”, but it later emerged that he had met Mr Kislyak during the campaign.
Mr Sessions denied any wrongdoing, but removed himself from an FBI inquiry into Russia’s alleged interference in the election.
Meanwhile Mr Trump and some Republicans have called for an investigation into intelligence leaks, including the leak that revealed details of Mr Flynn’s phone calls to the Russian ambassador.
Trump Russia claims: FBI’s Comey confirms investigation of election ‘interference’