Relatives of a black woman who was killed by police through her bedroom window are calling for federal officials to investigate the shooting.
A lawyer for the family on Monday said the white officer should be “vigorously prosecuted” as the local police department was “clearly incompetent”.
Atatiana Jefferson was killed after police responded to a non-emergency call from a neighbour on Saturday.
Body cam footage shows the officer shooting within seconds of seeing her.
Allegations of police brutality in black communities have been a longstanding issue in the US.
In its initial statement, the Fort Worth Police Department said the officer had “perceived a threat” when he drew his weapon.
On Monday Fort Worth police chief Ed Kraus told reporters that he had intended to meet the officer that morning to fire him, but the officer had resigned before he could do so.
Earlier Ms Jefferson’s sister, Ashley Carr, paid tribute to her in a news conference. “She was a smart, ambitious, kind person with a nurturing spirit,” Ms Carr said. “She was killed by a reckless act of a Fort Worth police officer.”
She called for a federal investigation into her death. Lee Merritt, a civil rights lawyer who is representing the family, said: “The investigation should be handled by someone other than the Fort Worth Police Department.”
He added that the department was “is on track to be one of the deadliest police departments in the United States”.
Fort Worth residents held a protest outside Jefferson’s home Sunday evening. First planned as a vigil, the gathering became a demonstration as residents demanded justice for the 28-year-old victim.
Participants held candles and chanting: “No justice, no peace.” Like Jefferson’s family, many called for the officer to be fired and criminally prosecuted.
“State sanctioned violence has always been a culture for black people,” said protester Michelle Andersen, at Sunday’s gathering. “It’s not about a training issue.”
Fort Worth Mayor Betsy Price was present at the vigil, but left after she was approached by protesters shouting “lock him up”, in reference to the unidentified officer, CBS News reported.
What happened Saturday?
The shooting happened at about 02:30 local time (07:30 GMT) on Saturday.
The body cam footage of the incident shows police searching the perimeter of Jefferson’s property, before noticing a figure at the window. After demanding that the person put their hands up, an officer then fired through the glass.
Ms Jefferson had been playing video games with her eight-year-old nephew before she went to investigate the noise outside the window and was shot, said a lawyer representing her family.
The officers involved did not park their marked cars in front of her house and did not identify themselves as police, officials said.
The man who called police, James Smith, 62, told local media he was trying to be a good neighbour.
“If I had never dialled the police department, she’d still be alive.” Mr Smith told local media. “It makes you not want to call the police department.”
The officer is expected to be interviewed by the police department’s major case unit on Monday.
Another tragedy in Dallas
Jefferson’s murder comes two weeks after Dallas police officer Amber Guyger, 31, was found guilty of murdering 26-year-old Botham Jean.
Last year Guyger shot and killed Jean as he sat eating ice cream on his apartment sofa, less than 35 miles (55km) from Saturday’s incident. Guyger testified she mistakenly thought she was in her own flat and believed Jean to be an intruder.
At trial, Guyger admitted to shooting “an innocent man”.
“This is a victory for black people in America,” said Mr Merritt – the lawyer who is also representing Jefferson’s family. “Police officers are going to be held accountable for their actions.”