The president and first lady traveled to University Medical Center, meeting with victims before his remarks with local officials at the Las Vegas Metropolitan Police Department.
"We grieve the loss of the law enforcement personnel who were killed in this vicious attack," Trump said. "Many families will go to bed tonight in a world that is suddenly empty."
He praised police officers who responded to the scene, including those who were off-duty at the concert as well as "civilian heroes."
"When everyone else was crouching, officers were standing up as targets, trying to direct people to tell them where to go," Trump said.
"When the worst of humanity strikes ... the best of humanity responds."
Fifty-eight people died Sunday when a gunman opened fire from the 32nd floor of the Mandalay Bay Resort and Casino across the street from the concert venue. Some 22,000 people had gathered at the outdoor venue to attend a country music festival. Some 527 people were injured in the hail of bullets.
"Words cannot describe the bravery that the whole world witnessed on Sunday night. Americans defied death and hatred with love and courage."
"A grateful nation thanks you," Trump concluded, adding that the bravery on display Sunday night should inspire the country to "show more love for the people who grace our lives."