Robert Mueller confirmed to the House judiciary committee that a criminal investigation had been launched.
Edward Snowden, 29, has admitted leaking information about National Security Agency (NSA) programmes that seize data from US internet and telephone firms.
Meanwhile, US senators briefed on the programmes have largely defended them.
Edward Snowden, who has pledged to fight any attempt to extradite him to the US, fled his home in Hawaii for Hong Kong shortly before reports of the top secret programmes were published by the Guardian and Washington Post newspapers last week.
China says it has “no information to offer” on the leaker’s whereabouts.
Edward Snowden, a former NSA contract computer technician, has admitted giving the newspapers information about NSA programmes that seize vast quantities of data from US internet and telephone companies.
In testimony on Thursday, Robert Mueller told the judiciary committee the leak caused “significant harm to our nation and to our safety”.
The FBI director, who is due to step down in September after 12 years in the job, said intelligence gathered following the leaks showed plotters were adapting to the revelations.
“One of my problems is that we’re going to… lose our ability to get their communications,” Robert Mueller said.
“We are going to be exceptionally vulnerable.”
He also stressed the phone records programme collected “no content whatsoever”.
Some committee members remained unconvinced by Robert Mueller’s defense.
Representative John Conyers, the committee’s top Democrat, said he feared the US was “on the verge of becoming a surveillance state”.
Robert Mueller said if the programmes had been place before the 9/11 attacks, they might have uncovered the plot.
“That opportunity would have been there,” he said.
But John Conyers replied: “I am not persuaded that that makes it OK to collect every call.”
The FBI director also told lawmakers Edward Snowden was the “subject of an ongoing criminal investigation” related to the leaks but would not give details on the status of the case.
Meanwhile, senators leaving a closed-door briefing with General Keith Alexander of the NSA largely defended the programmes.
Democrat Ben Nelson of Nebraska insisted procedures were already in place to protect Americans from government snooping and that the revelations in the news media had mischaracterized the programmes.
“It is misunderstood that American private information, emails and phone calls are being rummaged through by the government – that is not true,” he said.
“Only when there is probable cause given with a court order of a federal judge can they go into the content of phone calls and emails in order to be able to disrupt a terrorist plot.”
Tennessee Republican Senator Bob Corker told reporters lawmakers were given “some specific and helpful information about how these programmes have helped keep Americans safe”.
Senate intelligence committee chairwoman Dianne Feinstein, a California Democrat, predicted the Senate would consider legislation to curb contractors’ access to secret data.
In an interview at an undisclosed Hong Kong location published in the South China Morning Post on Wednesday, Edward Snowden said he believed there had been more than 61,000 NSA global hacking operations which targeted powerful “network backbones”.
He vowed to fight extradition to the US.
“All I can do is rely on my training and hope that world governments will refuse to be bullied by the United States into persecuting people seeking political refuge,” the paper quoted Edward Snowden as saying.
“Things are very difficult for me in all terms, but speaking truth to power is never without risk,” he said.
“It has been difficult, but I have been glad to see the global public speak out against these sorts of systemic violations of privacy.”
Who is Edward Snowden?
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