Revd Bryan Carter, from Concord Baptist Church which regularly sees congregations of more than 3000 people, was speaking after five white police officers were murdered when gunman Micah Johnson opened fire at a civil rights rally in the Texan city last week.
Micah Johnson was later killed in a police shoot-out.
The murders came after white police officers killed two black men earlier that week in Minnesota and Louisiana.
President Barack Obama, himself African-American, publicly condemned racial bias within police after the killings of Philando Castile and Alton Sterling, but also praised police for the often dangerous work that they do.
Mr Obama is now set to visit the families of the white police officers murdered in Dallas and speak at an interfaith memorial
Revd Bryan Carter told the BBC: "We are the tipping point and it could go either way. So it's important for us as a nation for us to try and figure out how do we not miss this moment?
"How do we make the changes that are needed and are necessary so that we don't go off on the wrong side?"
