UPDATE 2.42pm: As he prepared to travel to Las Vegas, Donald Trump said it was a "sad day".
The US president added: "It's a very sad thing. We are going to pay our respects and to see the police who have done really a fantastic job in a very short time."
He told reporters before departing the White House that authorities are "learning a lot more" about Paddock, and it would be "announced at an appropriate time".
"It's a very, very sad day for me personally," he said.
Mr Trump was joined by US first lady Melania Trump.
House majority leader Kevin McCarthy said he and congressman Mark Amodei, a Nevada Republican, would also make the trip.
UPDATE 10.59am: The Las Vegas gunman's girlfriend Marilou Danley who was in the Philippines at the time of Sunday night's shooting, may have been sent away by Stephen Paddock so as not to interfere with his plan.
Police are still trying to find out why a man with no record of violence or crime would kill 59 people and leave 527 others injured after opening fire on a concert crowd from a high-rise hotel.
Ms Danley, 62, first arrived in the Philippines on September 15, according to immigration documents.
She departed on September 22 then returned three days later on a flight from Hong Kong. She was travelling on an Australian passport.
Ms Danley's Australia-based sisters believe Paddock sent her away to prevent her from interfering with his plans.
Australia's Channel 7 TV network interviewed the sisters with their faces obscured and their names withheld. They said they believe their sister could not have known about his ideas.
One of the women said Ms Danley is "a good person" who would have stopped Paddock had she been there.
Another of the sisters, who live near Brisbane, Queensland, said they believed Marilou knew Paddock had guns, but not as many as he had.
Paddock transferred $100,000 (€85,000) to the Philippines in the days before the shooting, a US official said.
Investigators are still trying to trace that money and looking into a least a dozen financial reports over the past several weeks that showed Paddock gambled more than 10,000 (€8,500) per day, the official said.
As for what may have set Paddock off, retired FBI profiler Jim Clemente speculated that there was "some sort of major trigger in his life - a great loss, a break-up, or maybe he just found out he has a terminal disease".
Mr Clemente said a "psychological autopsy" may be necessary to try to establish the motive.
If the suicide did not destroy Paddock's brain, experts may even find a neurological disorder or malformation, he said.
He said there could be a genetic component to the slaughter: Paddock's father was a bank robber who was on the FBI's most-wanted list in the 1960s and was diagnosed as a psychopath.
"The genetics load the gun, personality and psychology aim it, and experiences pull the trigger, typically," Mr Clemente said.
Paddock had no known criminal record, and public records showed no sign of financial troubles.
UPDATE 9am: The girlfriend of the gunman who killed 59 people on the Las Vegas Strip is being questioned by police after returning to the US from the Philippines.
Sheriff Joseph Lombardo said investigators are hoping to get some insight from Marilou Danley on why Stephen Paddock opened fire on a concert crowd from a high-rise hotel room.
Ms Danley had been out of the country for weeks before the shooting but had been named as "a person of interest".
A law enforcement official said she arrived late on Tuesday night on a flight from Manila in Los Angeles, where FBI agents were waiting for her.
On Wednesday, President Donald Trump was due to visit Las Vegas to meet public officials, first responders and some of the 527 people who were injured in the attack.
Earlier: The gunman who killed 59 people in Las Vegas had planned the massacre so meticulously that he set up a camera in the peephole of his hotel room in an apparent attempt to spot anyone coming for him, investigators said.
Stephen Paddock also transferred $100,000 overseas just days before he opened fire on crowds attending an outdoor music festival.
The 64-year-old sprayed bullets on revellers enjoying the Route 91 Harvest Festival from the 32nd floor of the Mandalay Bay Hotel and Casino on Las Vegas Strip.
Paddock, from Mesquite, Nevada, killed himself before officers stormed Room 135 in the gold-coloured glass skyscraper.
Las Vegas sheriff Joseph Lombardo said he is "absolutely" confident investigators will establish why the big-spending gambler carried out the attack - the deadliest mass shooting in modern US history.
The cameras Paddock set up at the Mandalay Bay hotel were part of his extensive preparations that also included stockpiling nearly two dozen guns before the attack.
"I anticipate he was looking for anybody coming to take him into custody," Lombardo said.
"The fact that he had the type of weaponry and amount of weaponry in that room, it was pre-planned extensively," the sheriff said, "and I'm pretty sure he evaluated everything that he did and his actions, which is troublesome."
Undersheriff Kevin McMahill told reporters that Paddock also set up two cameras in the hallway outside his room so he could watch for anyone approaching.
He said Paddock fired on and off for nine to 11 minutes and unleashed about a dozen volleys. The first call about shots fired came in at 10.08pm and the gunfire stopped at 10.19pm.
In addition to the cameras, investigators found a computer and 23 guns in the hotel room. Officials said Paddock had devices attached to 12 weapons that allow semiautomatic rifles to mimic fully automatic gunfire.
Nineteen more guns were found at Paddock's Mesquite home and seven at his Reno house.
Authorities named the gunman's girlfriend, Marilou Danley, who was out of the country at the time of the shooting, as a "person of interest" and said the FBI would be bringing her back to the US on Wednesday for questioning.
Investigators are still trying to trace the $100,000 (€85,000) Paddock transferred to the Philippines in the days before the shooting, and are also looking into a least a dozen reports over the past several weeks that said Paddock had gambled more than 10,000 dollars per day, a US official said.
More than 500 people were injured in the rampage, some by gunfire, some during the chaotic escape. At least 45 patients at two hospitals remained in a critical condition. All but three of the dead had been identified by Tuesday afternoon.
Country music star Jason Aldean was performing on Sunday night at the end of the three-day festival in front of a crowd of more than 22,000 when the gunman opened fire from inside the 44-floor hotel across the street.
Paddock had checked into the hotel room on Thursday, authorities said.
People attending the country music concert described scenes of horror as they realised that what they first thought were fireworks were actually gunshots.
Harrowing video footage showed Aldean stopping his performance after an initial volley of shots could be heard.
After a pause, the gunman fired another volley, with the muzzle flashes visible from the casino as victims fell to the ground, while others fled in panic.
Jason Sorenson, of Newport Beach, California, said he first realised something was wrong when musicians left the stage.
He ran and said "we saw people with blood all over their shirts".
Brandon Clack, of La Palma, California, said he heard many shots fired and the shooting that "went on for a long time, like 10 minutes".
Concertgoers fled into casinos and crammed into cars to get away from the shooting.
Police shut down busy Las Vegas Boulevard, and federal and state authorities converged on the scene.
Interstate 15 was briefly closed, and flights at McCarran International Airport were suspended.
Hospital emergency rooms were jammed with the wounded.
The dead included at least three off-duty police officers from various departments who were attending the concert, authorities said.
Two on-duty officers were wounded, one critically, police said.
The FBI discounted the possibility of international terrorism early on, even after the Islamic State claimed responsibility for the attack.
President Donald Trump called the gunman a "very, very sick individual" and suggested he was ready to discuss gun laws "as time goes by".
Speaking to reporters on Tuesday, he called the gunman "demented" and said "we're looking into him very seriously" and praised police in Las Vegas.
Mr Trump stressed the shooting was a tragedy.
Asked about US legislation, the president said "we'll be talking about gun laws as time goes by".