President Barack Obama urged Americans rattled by a week of violence and protests to find "open hearts" and new empathy on Tuesday in a speech in Dallas that seesawed between honoring police officers for their bravery and decrying racial prejudice that can affect their work.

Obama stood next to five empty chairs for the white police officers killed last week by a black man seeking vengeance for police killings. Behind him, underscoring his message of unity: Dallas police officers, a racially diverse church choir and local officials who ranged from black Police Chief David Brown to former President George W. Bush, a Dallas resident.

Obama sought to reassure the nation that he understands the impact of the unsettling events of the past week - including the killing of two black men by police officers as well as the Dallas attacks.

Videos of the events have "left us wounded and angry and hurt", he said.

"It is as if the deepest fault lines of our democracy have suddenly been exposed, perhaps even widened."

"Dallas, I'm here to say we must reject such despair. I'm here to insist that we are not as divided as we seem. And I know that because I know America. I know how far we've come against impossible odds," he said.

The president spoke steps away from the empty chairs for the men killed by a sniper, a former Army reservist, on July 7 while they were protecting hundreds of people protesting the killings of black men in Louisiana and Minnesota.

The shooter, Micah Johnson, was eventually killed when police sent in a robot bomb. Johnson, 25, said he was motivated by revenge.

"The soul of our city was pierced," Mayor Mike Rawlings said, as he welcomed the president and a line of public officials, including Bush, who attended with his wife, Laura, Vice President Joe Biden and his wife, Jill, and Brown.

The group on stage capped the ceremony by holding hands and swaying to the Battle Hymn of the Republic.

"Too often we judge other groups by their worst examples, while judging ourselves by our best intentions," Bush said. "And this has strained our bonds of understanding and common purpose."

Bush and other speakers paid tribute to the fallen officers : Brent Thompson, a 43-year-old newlywed; Patrick Zamarripa, 32, a Navy veteran who served in Iraq; Michael Krol, 40, an athlete and basketball lover; Michael Smith, 55, a former Army Ranger and father of two, and Lorne Ahrens, whose wife is a detective.

The chief spent part of his time reciting Stevie Wonder's I'll Be Loving You Always to to express his affection for his officers.

For Obama, the moment was a chance to try to defuse what some have described as a national powder keg of emotions over race, justice, gun violence and policing. The president positioned himself as both an ally of law enforcement and a sympathizer of the Black Lives Matter group.