"In all but one of the cases the suspects have been apprehended," Mr Kasingye said.
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Uganda police say they have arrested a number of suspects over a recent spate of killings of women near the capital, Kampala.
The Inspector General of Police, Kale Kayihura, said that a suspect had confessed to killing eight women on the orders of businessmen.
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The murders were for ritual sacrifices, Gen Kayihura told residents of Nansana municipality.
Local media say 17 women have been killed in a gruesome manner since May.
Police spokesman Asan Kasingye told the BBC that while the murders occurred in the same district, they were not all related.
He said that in the majority of cases, the victims were sex workers who had been raped and strangled in isolated places in "the wee hours of the morning".
"Two were students," he said, adding that in five cases the women had been killed by their estranged partners.
Mr Kasingye said the municipalities were at least 60 km (40 miles) apart.
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He said that Gen Kayihura was reacting to local media reports that the police had failed to apprehend the culprits.