AURORA, Colo. — Despair all around him, President Barack Obama on Sunday offered hugs, tears and the nation’s sympathy to survivors of the Colorado shooting rampage and to families whose loved ones were shot dead. He looked for hope in the heartbreak, insisting a brighter day will come for the grieving and declaring that “much of the world is thinking about them.”

In dramatic detail, Obama offered a glimpse inside the horror that took place in the Denver-area movie theater early Friday, relaying a story he said spoke to the courage of young Americans. With two fingers pressed to his own neck, Obama recalled how one woman saved the life of a friend who had been shot by keeping pressure on a vein that had “started spurting blood” and by later helping carry her to safety.

In private, Obama visited one by one with anguished families gathered at a hospital and wounded patients recovering in intensive care. He emerged before the TV cameras and kept his focus on the lives and dreams of the fallen and the survivors, not the sole shooting suspect or his “evil act.”

“I come to them not so much as president as I do as a father and as a husband,” said Obama, addressing reporters from a hospital hallway after his visits. “The reason stories like this have such an impact on us is because we can all understand what it would be to have somebody we love taken from us in this fashion.”

For a president nearing the end of his term and seeking a second one, it was another grim occasion for him to serve as national consoler in chief, a role that has become a crucial facet of the job. National tragedies compel presidents to show leadership and a comforting touch — or risk a plummeting public standing if they cannot match the moment.

The massacre in the Aurora movie theater left 12 dead and 58 wounded. It also temporarily silenced a bitter campaign fight for the White House between Obama and Republican Mitt Romney.

Both men were searching for the right time and manner to re-enter the political debate.

Obama’s stop in Colorado — which happens to be a key electoral state in the race — came as he was about to shift into a mix of campaign fundraisers and official travel across the West starting Monday. Romney resumed political activities Sunday in California, where he courted Republican donors in three fundraisers in the San Francisco area.

“I know the president is in Colorado today,” Romney told supporters while keeping a subdued tone. “He’s visiting with families and friends of the victims, which is the right thing for the president to be doing on this day — appreciate that.”

Obama said his conversations with family members were filled with memories of brothers, sons and daughters who had left their mark on others. He said there were laughs as well as tears.

Jordan Ghawi, brother of shooting victim Jessica Ghawi, tweeted that Obama was already familiar with his sister’s story before sitting down with him but wanted to learn more.

“My main task was to serve as a representative of the entire country and let them know that we are thinking about them at this moment and will continue to think about them each and every day,” Obama said. “The awareness that not only all of America but much of the world is thinking about them might serve as some comfort.”

A single suspect, James Holmes, is being held without bond on suspicion of multiple counts of first-degree murder after the shooting rampage, which occurred minutes into a premiere of “The Dark Knight Rises” Batman movie early Friday in this suburb outside Denver.

Obama said he assured the families that even though the suspect behind “this evil act has received a lot of attention over the last couple of days, that attention will fade away. And in the end, after he has felt the full force of our justice system, what will be remembered are the good people who were impacted by this tragedy.”

The president’s most vivid lines came in describing the story of two friends, 19-year-old Allie Young and her best friend, 21-year-old Stephanie Davies. Both were in Young’s hospital room when Obama visited.

Obama recounted that when the gunman entered the movie theater and threw canisters of gas at the start of his killing spree, Allie stood up to warn people.

“And she was shot in the neck, and it punctured a vein, and immediately she started spurting blood,” Obama said.

“And apparently, as she dropped down on the floor, Stephanie — 21 years old — had the presence of mind to drop down on the ground with her, pull her out of the aisle, place her fingers over where Allie had been wounded, and applied pressure the entire time while the gunman was still shooting,” Obama said.

The president said Davies eventually joined others in carrying her friend to an ambulance. He said Young was going to be fine.

“As tragic as the circumstances of what we’ve seen today are, as heartbreaking as it is for the families, it’s worth us spending most of our time reflecting on young Americans like Allie and Stephanie,” Obama said. “They represent what’s best in us, and they assure us that out of this darkness a brighter day is going to come.”

The task of articulating sorrow and loss has become a familiar one for Obama.

In November 2009, he led mourners at a service for victims of the mass shooting at Texas’ Fort Hood. In January 2011, he spoke at a memorial for the six victims killed in Tucson, Ariz., when a gunman attacked Rep. Gabrielle Giffords as she met with constituents.

The following April, when some 300 people were killed in a multistate series of tornadoes, Obama flew to Tuscaloosa, Ala., to commiserate with residents whose homes were in ruins. A month later, Obama went to Joplin, Mo., after a monster twister claimed 161 lives.