"The accused is probably a drug addict residing in the same Badarpur slum where the incident was reported from Friday evening," a Delhi Police officer said Saturday.
"We are on the lookout for a single assailant who might have involved behind the brutalisation," he added.
Additional Commissioner of Police Ajay Chaudhary said that around 400 houses in the slum have been searched to nab the accused.
"We are working on the case and the accused will be nabbed soon," Chaudhary said.
The minor girl, who was allegedly raped, had apparently resisted the assault, which may be the reason for her serious throat injuries, her uncle said Saturday.
"When we found the girl, she had held herself steadfast to the toilet wall. Her throat had been slit. It clearly appeared that she had resisted the assault," the girl's uncle told IANS.
Doctors treating the minor girl said that she is not being able to swallow food due to the sharp cut on her neck, which has been operated on.
The victim's family held a protest on the Mehrauli-Badarpur Road Saturday. They blocked traffic for about an hour and demanded immediate action from the administration.
"There is severe damage to the anal canal. We are waiting for medical reports to confirm whether it was a rape, as she suffered severe rectal-vaginal injuries. Though there is evidence of penetration, we don't know whether it was a foreign object," said Biplab Mishra, trauma surgeon at All India Institute of Medical Sciences (AIIMS) Trauma Centre.
"She is stable right now. She is still in the ICU at the AIIMS Trauma Centre. She has coped well with life-saving surgery, performed yesterday (Friday), which lasted nearly three hours," Mishra said.
A passer-by had spotted the six-year-old lying in an unconscious state near a public toilet in Badarpur area of south Delhi Friday afternoon, who later informed the police.
"When the girl's cousin, who first got to know about the incident, went to see her, he found a deep injury on her neck. She was completely naked," the victim's uncle said.
The girl was taken to a nearby medical store, from where she was shifted to AIIMS Trauma Centre, he said. She had suffered critical injuries and had to undergo a three-hour-long surgery to save her life, Friday night.
The girl's father is a balloon seller. The family from Uttar Pradesh had been living in a slum cluster near National Thermal Power Corporation plant in Badarpur for the past 25 years.
The girl has seven siblings.