Speaking haltingly because of her injuries, Ms Giffords opened testimony at the first congressional hearing on gun violence since a gunman shot dead 20 children and six adults at an elementary school in Newtown, Connecticut.
Responding to outrage across the country, President Barack Obama has asked Congress to pass the largest package of gun restrictions in decades.
Ms Giffords, who had been targeted in a separate shooting in Tuscon, Arizona, said: "This is an important conversation for our children, for our communities, for Democrats and Republicans.
"Speaking is difficult. But I need to say something important.
"Violence is a big problem. Too many children are dying – too many children.
"We must do something. It will be hard. But the time is now."
Accompanied by her husband, former astronaut Mark Kelly, she concluded: "You must act. Be bold, be courageous.
"Americans are counting on you. Thank you."