The F.B.I. director, James B. Comey, took the extraordinary step on Monday of announcing that the agency is investigating whether members of President Trumps campaign colluded with Russia to influence the 2016 election. Mr. Comeys testimony before the House Intelligence Committee created a treacherous political moment for Mr. Trump, who has insisted that Russia is fake news that was cooked up by his political opponents to undermine his presidency. Mr. Comey placed a criminal investigation at the doorstep of the White House and said officers would pursue it no matter how long that takes. Joined by Adm. Michael S. Rogers, the director of the National Security Agency, Mr. Comey also dismissed Mr. Trumps claim that he was wiretapped by his predecessor during the campaign, a sensational accusation that has served as a distraction in the public debate over Russian election interference. Taken together, the two provided the most definitive statement yet that Mr. Trumps accusation was false. The New York Times and other news organizations have reported the existence of the investigation into the Trump campaign and its relationship with Russia, but the White House dismissed those reports as politically motivated and rallied political allies to rebut them. Mr. Comeys testimony on Monday was the first public acknowledgment of the case. The F.B.I. discloses its investigations only in rare circumstances, when officials believe it is in the public interest. This is one of those circumstances, Mr. Comey said. Mr. Comey said the F.B.I. was investigating the nature of any links between individuals associated with the Trump campaign and the Russian government, and whether there was any coordination between the campaign and Russias efforts. American intelligence agencies concluded in January that President Vladimir V. Putin of Russia personally ordered a covert effort to hurt Hillary Clintons chances and aid Mr. Trump. That included hacking political targets, including the Democratic National Committee, and releasing embarrassing emails through the website WikiLeaks. The White House dismissed most of Mr. Comeys testimony, saying there was no coordination between the Trump campaign and Russia and so there was nothing to investigate. Sean Spicer, the White House press secretary, said the more pressing issue was who disclosed classified information about Mr. Trumps advisers to journalists, suggesting that they might have been former members of the Obama administration.