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 FBI’s director said the gunman was radicalised through the internet.
Meanwhile Donald Trump said he would suspend immigration from certain areas of the world to the US.
The presumptive Republican presidential candidate also renewed his call for a temporary ban on Muslims entering the country.
The US authorities say gunman Omar Mateen pledged allegiance to IS shortly before the attack in Florida.
However, the extent of any links to IS remains unclear.
Speaking in Washington, Mr Obama 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 deadliest mass shooting in recent US history ended when police shot Mateen dead. The attack also left 53 people injured.
Orlando Regional Medical Centre said on Monday that a number of the victims being treated there remained critically ill, and five patients were in a grave condition.
Responding to the Orlando shootings, Mr Trump reiterated his proposal to ban foreign Muslims from entering the US.
“We cannot continue to allow thousands upon thousands of people to pour into our country, many of whom have the same thought process as this savage killer.”
Mr Trump said: “When I’m elected I will suspend immigration from areas of the world where there is a proven history of terrorism against the United States, Europe or our allies.”
He also spoke out against any move to increase gun controls, saying he would be “always defending” the Second Amendment which protects “the right of the people to keep and bear arms”.
AR-15s in the US in 2012 (estimated)
45 rounds per minute
26 people killed by AR-15 in Sandy Hook in 2012
0 days’ wait needed to obtain one in Florida
Meanwhile presumptive Democratic candidate Hillary Clinton promised to make stopping “lone wolf” attacks a top priority.
Mrs Clinton called for action to stop militants getting hold of assault rifles, saying weapons of war had no place on America’s streets.
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.
The owner of a gun shop where Mateen recently bought two guns said he had passed a full background check when purchasing the weapons.
“If he hadn’t purchased them from us I’m sure he would have gotten them from another local gun store,” Edward Henson from the St Lucie Shooting Center told reporters.
What happened on the night?
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 police officer working at the club fought Mateen in a gun battle before police reinforcements arrived.
Forced to retreat into a toilet, Mateen took hostages, Orlando police chief John Mina said.
Another 15 or so people were in another toilet, across the hallway, Orlando Mayor Buddy Dyer said.
Believing Mateen would kill again imminently, police used explosives and an armoured vehicle to break through a wall of the building and survivors began streaming through the hole they had created.
Mateen himself followed them out shooting and was killed, police say.
Cities around the world have been flying rainbow gay pride flags and illuminating buildings in solidarity with the victims of the shooting in Florida.
Who were the victims?
The names of 48 of the 49 victims have now been released: 41 men and seven women. They include:
- Edward Sotomayor, 34, who worked for a company that organised gay cruises
- Stanley Almodovar, 23, a pharmacy technician who was remembered as “kind and sassy”
- Kimberly Morris, 37, who had only recently moved to Orlando and worked at Pulse as a bouncer
- Luis Vielma, 22, who worked at the Harry Potter section at Universal Studios – author J K Rowling paid tribute to him online
- Eddie Justice, 30, who sent his mother a series of text messages while inside the club – read more on him here
- Akyra Murray, 18, who graduated from high school a week ago – her school described her as a “superstar”
The Pulse nightclub was holding its Latino night when the attack took place and many of the victims have Latino or Hispanic names.
LGBT community under siege