"As a mark of respect for the victims of the senseless acts of violence... I hereby order that the flag of the United States shall be flown at half-staff at the White House and upon all public buildings and grounds, at all military posts and naval stations, and on all naval vessels... until sunset, July 25," Obama said in a presidential proclamation.
US flags will also be flown at half-staff at US embassies, consular offices and other facilities abroad, including all military facilities and naval vessels and stations.
At least 12 people were killed and around 40 others wounded in the midnight rampage at a movie theater in the Denver area showing "The Dark Knight Rises."
Obama dropped a planned re-election campaign event in Fort Myers, Florida and instead spoke there about the shooting spree, saying the killings were "beyond reason."
He cut his appearance short and headed to the airport to board Air Force One back to the White House.
His campaign team said they were pulling all contrast ads -- commercials contrasting Obama with his Republican rival Mitt Romney -- in Colorado, a key battleground state ahead of November's election.
Romney's team said it was taking similar action.
Police arrested the shooting suspect - identified as 24-year-old James Holmes - without encountering resistance by his car at the rear of the theater, in Aurora, a suburb of the city of Denver, in Colorado.
SHOOTING SUSPECT 'A LONER'
The suspected gunman in the Colorado movie-theater massacre emerged Friday as a 24-year-old medical student with a reputation as a loner going back to his southern California childhood.
James Holmes was enrolled since June 2011 as a student in neurosciences at the University of Colorado, but was in the process of withdrawing, the Denver Post newspaper quoted a university spokesman as saying.
In a photo released by the university, Holmes appears smirking in a burnt-orange T-shirt and slightly disheveled hair.
Another photo, from his San Diego high school yearbook, depicted Holmes in a dark suit, flashing a toothy smile. He graduated from Westview High School in San Diego in 2006.
The FBI described Holmes as a white male, 6-foot-3 (1.9 meters) tall, born on December 13, 1987, with no significant criminal record and no links to terrorism.
Police in Aurora, Colorado, told reporters his only black mark in the city was a speeding ticket in 2011.
In an apartment rental application he submitted in early 2011, Holmes described himself as a "quiet and easy-going" student, the Denver Post said on its website (www.denverpost.com).
"No one knew him. No one," it quoted a pharmacy student living in the same building -- reserved for medical students, faculty and staff -- in Aurora as saying.
The student, who only gave his name as Ben, said Holmes kept to himself and would not say hello or acknowledge other people in the hallway.
Ben also revealed he had called police shortly after midnight -- coincidentally around the time of the massacre at a Batman premiere -- to report a song blaring from inside Holmes' apartment.
Ben could not make out the song, but it appeared to be playing on repeat.
Tom Mai, a next-door neighbor of the Holmes family in San Diego, remembered Holmes as a shy teenager who did not play or socialize with other youngsters in the neighborhood, the San Diego Union-Tribune newspaper said.
"He said that he last saw him two years ago when he came home during summer recess from college," it said on its website (www.utsandiego.com). "The family, he said, was nice and involved with a Presbyterian church."
Holmes graduated from the University of California in Riverside in 2010 with a degree in neuroscience, said its director of communications Kris Lovekin, who added she could not release any further information about him.
Local judicial officials quoted by the Union-Tribune said Holmes had no past or pending court cases in San Diego.
Mashable.com, which monitors social media, said Holmes was "an online ghost" with no apparent presence on sites like Facebook or Twitter, although people sharing Holmes' name found themselves suddenly bombarded with attention.
In a statement, Holmes' family said they were cooperating with investigators.
"We are still trying to process this information and we appreciate that people will respect our privacy," the family said, after Holmes' mother Arlen confirmed her son was the suspected shooter.
