In the televised address the President said "The federal government stands ready to do everything necessary to bring whoever's responsible for this heinous crime to justice.
"I'm sure many of you who are parents had the same reaction as I did when you first heard this news: 'What if it had been my daughters at the theatre?'
"Michelle and I will be fortunate to hug our children a little tighter this weekend, as I'm sure you will do with your children."
He added that the government "will take every step possible" to ensure the safety of all Americans.
James Holmes, a 24-year-old loner who recently quit medical school, was arrested after the massacre at the midnight screening of the latest Batman movie.
Ten people were killed at the scene and another two died later of their injuries.
The great-aunt of six-year-old Veronica Moser told reporters at the cinema where the shooting happened that the girl's mother, Ashley Moser, was still critically ill in hospital and could be paralysed after being shot in the neck.
Others victims already named include 24-year-old Jessica Redfield, a promising sports journalist; Alex Sullivan, who was preparing to celebrate his 27th birthday; US Navy sailor John Larimer; and 23-year-old Micayla Medek.
Jessica's brother, Jordan Ghawi, described how he heard the news his sister was caught-up in the shooting from his friend Brent who was with her in the cinema.
"He told me he was inside the theatre when some sort of incendiary or diversion device was deployed into the crowd, at which point the crowd began to rise out of their seats.
"Shots were fired. They dropped to the ground. My sister called 911, he attempted to call 911.
"My sister was struck by a round on the leg. He immediately, with his medical training, began to put pressure to that wound, to help stabilise her and she was screaming, and as he was on the ground, he took a round to the leg.
"And he realised my sister was no longer screaming. And he looked over and it appeared she had had a fatal shot direct to her head."
The family of Alex Sullivan released a statement celebrating the memory of their son.
"The Sullivan family lost a cherished member of their family today," it said.
"Alex was smart, funny and, above all, loved dearly by his friends and family. Today was his 27th birthday. They respectfully ask that the media allow them time to grieve privately."
Petty Officer Third Class John Larimer's comanding officer paid tribute to "an outstanding shipmate".
"A valued member of our Navy team, he will be missed by all who knew him. My heart goes out to John's family, friends and loved ones, as well as to all victims of this horrible tragedy," Commander Jeffrey Jakuboski said.
Petty Officer Larimer was a cryptologic technician and had been stationed in Aurora since October 2011.
Meanwhile, Christopher Nolan, director of The Dark Knight Rises, called it a "senseless tragedy" that was "unbearably savage".
The Oscar-nominated filmmaker cancelled the French premiere of the film and a media junket in Paris hours after the shootings.
"Speaking on behalf of the cast and crew... I would like to express our profound sorrow at the senseless tragedy that has befallen the entire Aurora community," he said.
The shooting halted campaigning in the US presidential race, but neither President Obama nor Republican challenger Mitt Romney addressed the volatile issue of gun control in America.
"There are going to be other days for politics," Mr Obama said from one key electoral state, Florida. From another one, New Hampshire, Mr Romney said much the same.
However, New York City Mayor Michael Bloomberg, a gun control advocate, said: "You know, soothing words are nice, but maybe it's time that the two people who want to be president of the United States stand up and tell us what they are going to do about it."
Twenty years ago, polls showed that a substantial majority of Americans - nearly 80% in 1990 - supported stricter limits on guns.
But now Americans appear evenly divided between those who want tougher restrictions and those who want to stick with current laws - which allow easy access to guns in many areas