The gunman, identified as Stephen Paddock, ended Sunday night's shooting spree, the deadliest in modern US history, by killing himself.
He left an arsenal of 42 guns but no clear clues as to why he staged the attack on a crowd of 20,000 from a 32nd-floor window of the Mandalay Bay hotel.
More than 500 people were injured, some trampled.
Federal, state and local investigators have found no evidence that Paddock, 64, had even incidental contacts with foreign or domestic extremist groups, and reviews of his history show no underlying pattern of lawbreaking or hate speech, a senior US homeland security official said on Tuesday.
"We cannot even rule out mental illness or some form of brain damage, although there's no evidence of that, either," the official said, speaking on the condition of anonymity to discuss the probe.
Paddock's brother, Eric, has described himself as equally mystified by the attack.
"It just makes less sense the more we use any kind of reason to figure it out," Eric Paddock said in a text message on Tuesday. "I will bet any amount of money that they will not find any link to anything ... he did this completely by himself."
He described his brother as a financially well-off enthusiast of video poker and cruises, with no history of mental health issues.
President Donald Trump told reporters on Tuesday that Paddock had been "a sick man, a demented man." He declined to answer a question about whether he considered the attack an act of domestic terrorism.
Trump was due to visit Las Vegas on Wednesday.
US officials discounted a claim of responsibility by the Islamic State militant group and said they believed Paddock acted alone.
Although police said they had no other suspects, Clark County Sheriff Joseph Lombardo said investigators wanted to talk with Paddock's girlfriend and live-in companion, Marilou Danley, who he said was traveling abroad, possibly in Tokyo.
The closest Paddock appeared to have ever come to a brush with the law was a traffic infraction, authorities said.
Las Vegas Police said they would next provide an update on the investigation at 1 pm PT (1900 GMT).
GUN DEBATE STIRRED
The attack stirred the fractious debate about gun ownership in the United States, which is protected by the Second Amendment to the Constitution, and about how much that right should be subject to controls.
Sunday's shooting followed the massacre of 26 young children and educators in Newtown, Connecticut, in 2012, and the slaying of 49 people at a gay nightclub in Orlando last year. The latter attack was previously the deadliest mass shooting in modern US history.
Democrats reiterated what is generally the party's stance, that legislative action is needed to reduce mass shootings. Republicans, who control the White House and both chambers of Congress, argue that restrictions on lawful gun ownership cannot deter criminal behavior.
"We'll be talking about gun laws as time goes by," said Trump, who strongly supported gun rights during his presidential campaign.
US Senate Democratic leader Chuck Schumer urged Trump to bring together both major parties to devise a solution to gun violence.
"I am requesting the president to call us together, Democrats and Republicans, to come up with a reasonable solution," Schumer told journalists.
Senate Republican leader Mitch McConnell said it was too soon after the attack to discuss "legislative solutions" to gun violence.
"It's particularly inappropriate to politicize an event like this, which just happened in the last day and a half," McConnell told journalists.
ATYPICAL KILLER
Paddock seemed atypical of the troubled, angry young men who experts said have come to embody the mass-shooter profile in the United States.
Public records on Paddock point to an itinerant existence across the US West and Southeast, including stints as an apartment manager and aerospace industry worker. He appeared to be settling in to a quiet life when he bought a home in a Nevada retirement community a few years ago.
Police said they found 23 guns in Paddock's suite at the Mandalay Bay hotel. They found another 19 firearms, explosives and thousands of rounds of ammunition at Paddock's home in Mesquite, 90 miles (145 km) northeast of Las Vegas.
A search of his car turned up a supply of ammonium nitrate, a fertilizer that can be formed into explosives and was used in the 1995 Oklahoma City bombing of a federal office building that killed 168 people, Lombardo said.
Chris Sullivan, the owner of Mesquite's Guns & Guitars shop, issued a statement confirming that Paddock was a customer who cleared background checks and said his business was cooperating with investigators.
Lombardo said investigators knew a gun dealer had come forward to say that he had sold weapons to the suspect, but it was not clear if he was referring to Sullivan. He said police were aware of other people engaged in those transactions, including at least one in Arizona.
