At least 58 people were killed in the deadliest mass shooting in modern US history on Sunday night, when a gunman opened fire on an open-air music festival from the 32nd floor of the Mandalay Bay hotel and casino on the Las Vegas strip.

A further 515 people were injured, Las Vegas police said, as casualty figures continued to rise. The death toll surpassed the shooting at the Pulse nightclub in Orlando in June 2016, when 49 people were killed.

The suspected gunman was identified as Stephen Paddock, a 64-year-old local man who police believe booked into the Mandalay Bay on 28 September. He was found dead after officers stormed his room, where they recovered more than 10 guns.

A brother of the suspect living in central Florida, Eric Paddock, said he was “dumbfounded”. “He’s not an avid gun guy at all,” the brother said. “The fact that he had those kind of weapons is just … he has no military background or anything like that.”

Speaking at the White House, Donald Trump called the attack “an act of pure evil”. He did not discuss possible motives for the attack, saying federal and local authorities would provide updates.

Nor did he call for new gun control measures or other government action to confront the US epidemic of mass shootings.

“America comes together as one and it always has,” Trump said. “We call upon the bonds that unite us: our faith, our family and our shared values.”

Trump said he would visit Las Vegas on Wednesday and directed that flags outside government buildings be flown at half-staff. He still planned to visit hurricane-devastated Puerto Rico on Tuesday.

The FBI said it had found “no connection with an international terrorist group”. The Clark County sheriff, Joe Lombardo, said police had found nothing to suggest a motive for the attack.

“We’ve checked all the federal databases and Nevada databases and we have no knowledge of this individual,” he said. “I can’t get into the mind of a psychopath at this point.”