Johnson spoke on Sunday morning, a day after demonstrators in major cities around the country again took to the streets last night to protest the police-involved killings of two African American men over the past week, Philando Castile in suburban St. Paul, Minnesota, and Alton Sterling in Baton Rouge, Louisiana.
Asked how the nation can build trust between police and civilians, Johnson called for more community policing.
"In these times, building bridges, conversations, community relationships between the community, between law enforcement, can and does work," Johnson said.
"We mourn the loss of five brave police officers in Dallas, and there have been incidents all across this country that have created a lot of anxiety," Johnson said. "Now is the time for healing, the time for mourning, and the time for building bridges and dialogue."
New York City Police Commissioner Bill Bratton, also speaking on "This Week," echoed Johnson's call for building bridges between law enforcement and the public.
"The idea is we need to find common ground in understanding the role of the police and the role of the public," Bratton said. "This is a shared responsibility, trying to bridge these differences that are becoming quite evident through many of these videos that are now becoming very frequent on our TV stations and in the public."
The New York City police commissioner also commented on the Dallas Police Department's use of a bomb-carrying robot to kill suspected gunman Micah Xavier Johnson, who targeted and killed law enforcement officers, on Thursday night. Bratton said he approves of the Dallas police chief's decision.
"I approve of the chief’s decision down there to use that robot so as to not put any additional officers’ lives at risk in that circumstance," Bratton said.
"That capability is there, but it is the first time that type of action has been initiated here in the United States and it deserves to be reviewed," Bratton said.