A gunman is currently at large after two police officers and one civilian were shot and critically wounded.
Speaking at a press conference, Mr Rawlings said: “Dallas once again is at the precipice looking into the hell of heartbreak as our police department was attacked this afternoon.”
He added the Dallas press has always been responsible, but “families come first, not the news” as he said he would not give details of the officers who were shot.
He said: “I continue to be upset at the lack of respect of our police, both in this city and our country.
“Now is the moment we can lift them up and I ask you to do this.”
Dallas Police Chief Renee Hall then gave an update on the police investigation.
She said the suspect is 29-year-old Armando Juarez who possibly fled the scene in a white pickup.
The shooting took place around 4.15pm local time (10.15pm GMT).
Officers were assisting an off-duty officer working on security arrest someone when the shooter opened fire.
A baseball game at nearby Dallas Lutheran High School is on lockdown while police search for the gunman.
The pupils are locked inside the school.
Helicopter video footage shows officers searching for the suspect in a nearby creek.
One person has been taken to Presbyterian Hospital in Dallas.
In 2016 Dallas had one of the deadliest ambushes on law enforcement in recent US history.
Five officers were shot and killed while patrolling a Black Lives Matter protest.