Gangs of thieves armed with automatic rifles and knives have been active in the city's sixth district, forcing residents to stand guard on rooftops at night, they said.
Thieves have broken into houses and tied and beaten residents before stealing their money and jewellery, killing those who tried to resist or called for help, worried locals said.
Several people have been killed by burglars in the past two weeks in the city's western area of Dasht-i-Barchi and its outlying villages, they said.
One resident said that his brother Sayed Rahman, a horse-cart driver and father of two children, was shot dead by masked thieves on the eve of the Muslim Eid-ul-Fitr festival when he called for help.
The intruders took away money worth ten US dollars and a tape-recorder.
"The number of armed thefts has increased so much in our area that we have to sit alert on our rooftops every night," another resident said.
Abdul Ghani Armani, Taliban police chief in the district, confirmed that two gangs of thieves had been operating in the western suburbs.
He said burglary cases had occurred in the villages of Qalai Qazi, Gul Khana and Char Qala recently.
"We have told the residents to maintain their security, to stay awake and call us either by shouting or by firing shotguns," the police chief said.
He said that 40 policemen on three pick-up vans were regularly patrolling the narrow unlit streets in an area of several thousand houses.
"No one has been killed, but cases of theft have been reported. The people are worried. It is our Islamic duty to remove their problems" he said.
"There is another group of five to six people armed with one Kalashnikov rifle who are active here. We have not yet been able to capture them despite continued efforts," Armani said.
Residents also reported cases of abduction for extortion in the city's ninth district. They said citizens were not allowed to carry guns or stay out during the night becasue of an eight-hour daily curfew.
The fundamentalist Taliban Islamic militia, which holds most of the country, boasts of having restored law and order after ousting the government of president Burhanuddin Rabbani in 1996.
About two-thirds of the Afghan capital Kabul was destroyed in Rabbani's time as a result of bitter fighting between rival mujahideen factions.
The Taliban police officer said the current problem in Kabul were partly linked to old enmities among the locals.