Gifford's husband, space shuttle Capt. Mark Kelly, sat between the first lady and Secretary of Homeland Security Janet Napolitano.
In a tone similar to President John F. Kennedy in his 1961 inauguration speech, Obama called upon the nation to respond with charity towards one another.
"We cannot and will not be passive in the face of such violence. We should be willing to challenge old assumptions in order to lessen the prospects of violence in the future," he said. "But what we can't do is use this tragedy as one more occasion to turn on one another.
"As we discuss these issues, let each of us do so with a good dose of humility," he added. "Rather than pointing fingers or assigning blame, let us use this occasion to expand our moral imaginations, to listen to each other more carefully, to sharpen our instincts for empathy and remind ourselves of all the ways our hopes and dreams are bound together."
The outpouring of support in Tucson Wednesday night was evident as thousands waited in line, some sleeping on the ground overnight, to enter the McKale Memorial Center.
The university set up an area to handle the overflow of students and other attendees who camped out on the sidewalk.
Giffords' office issued a statement in response: "The outpouring of support from the people of Arizona and Americans across the country has been truly moving. We appreciate everyone's thoughts and prayers during this difficult time. The resolution before the House today was a further reflection of the best of America -- one after another, members came to the floor, without party labels, in support of those impacted by this tragedy. They honored the fallen, those recovering, and the heroes who responded quickly to save lives. ... Even during the darkest times, our nation's capacity for kindness and fellowship reminds us of the best in people. To everyone who has expressed well wishes, we offer our most heartfelt thanks."
ABC News' Michael S. James, Amanda VanAllen and Leezel Tanglao contributed to this report.