"After the events of this week, Americans across the county are feeling a sense of helplessness, of uncertainty and of fear. These feelings are understandable and they are justified. But the answer must not be violence. The answer is never violence," said Lynch.
"Rather, the answer must be action: calm, peaceful, collaborative and determined action."
One of the suspects in the assault against Dallas police officers told hostage negotiators he was angry about recent fatal shootings of black men by police elsewhere in the United States and that he wanted to kill white people, especially police officers. Two civilians were also injured in the Dallas shootings.
"This has been a week of profound grief and heartbreaking loss," said Lynch.
Police spent hours negotiating with the gunman before he was killed by an explosive strapped to a police robot, according to Dallas Police Chief David Brown.
"Today, we are feeling the devastating loss of Dallas Area Rapid Transit Officer Brent Thompson and four other fallen officers whose names remain unreleased as we await notification of all the families," said Lynch.