There is no clear evidence that the Orlando gunman was directed by the so-called Islamic State group (IS), US President Barack Obama has said.
But the inquiry into the attack on the Pulse gay night club, in which 49 people were killed, is being treated as a terrorist investigation, he added.
The US authorities say gunman Omar Mateen pledged allegiance to IS shortly before the attack in Florida.
However, the extent of his links to IS remains unclear.
Speaking in Washington, the president said: "It does appear that at the last minute he [gunman Omar Mateen] announced allegiance to Isil [IS].
"But there is no evidence so far that he was in fact directed. This is certainly an example of the kind of home-grown extremism that all of us have been concerned about for a very long time."
The investigation
FBI Director James Comey told reporters in Washington that there were "strong indications of radicalisation and of potential inspiration by foreign terrorist organisations".
"We're highly confident this killer was radicalised at least in some part through the internet," he said.
In phone calls to the authorities from the nightclub, Mateen said he was carrying out the attack for IS but he also pledged allegiance to a suicide bomber for the al-Nusra Front group in Syria, and to the perpetrators of the Boston Marathon bombing, none of whom is linked to IS.
"We see no indication that this was a plot directed from outside the United States, and we see no indication that he was part of any kind of network," Mr Comey said.
Investigators are going through the killer's life, and especially his electronic devices, to try to understand his motivation, Mr Comey said.
The FBI director declined to use the gunman's name, as "part of what motivates sick people to do this kind of thing" was a desire for fame, he said.
"We are also working to understand what role anti-gay bigotry played in this attack," Mr Comey said.
Mr Comey detailed his organisation's prior contact with Mateen, and defended the FBI's investigations into him.
"I don't see anything in reviewing our work that our agents should have done differently," Mr Comey said, while promising transparency over the issue.
Mateen began shooting inside the club around 02:00 (06:00 GMT) on Sunday, when the club was holding a Latin night and was packed with revellers.
An off-duty officer working fought Mateen in a gun battle before police reinforcements arrived.
Cities around the world have been flying rainbow gay pride flags and illuminating buildings in solidarity with the victims of the shooting in Florida.
On Monday evening Londoners held a vigil in Old Compton Street in the heart of Soho.
Hundreds also gathered in Glasgow's George Square.