Police in Rwanda are investigating the murder of 15 women, most of them sex workers, amid speculation that a serial killer is at large. All the victims were strangled.

The mysterious deaths have puzzled the tiny east African republic and instilled fear among sex workers, whose trade is illegal but often seen as a way out of poverty.

Most of the women were killed in the capital, Kigali, in the past two months, police said. Two suspects were arrested last week, the Rwanda Focus newspaper reported, but detectives continue to search for a culprit or culprits.

Supt Theos Badege, a police spokesperson, said: "Rwanda national police is well aware of these mysterious incidents and measures have been undertaken to bring to justice all those responsible.

"Rwanda national police takes this as a serious case and a special team has been appointed to investigate thoroughly these incidents and produce the findings as soon as possible."

The victims include three women who were killed in broad daylight in a working class district of Kigali on 28 August. Two were known sex workers while the third is suspected to have been killed after she witnessed the murders of the others, local media reported.

The Rwanda Focus claimed that, according to several neighbours, another victim, Clementine Uwimbabazi, was found dead at her house with the words "I will stop once I have killed 400 prostitutes" carved into the flesh of her stomach.

Police dismissed this as a rumour, the paper added. "Conflicts over money and revenge following HIV/Aids contamination are apparently at the root of the problem," it quoted Badege as saying.

The Rwanda Focus also interviewed Flora Uwase, a sex worker and friend of Uwimbabazi. "I was the first to see her body, and you would have thought she was sleeping," she said. "The killer knew very well what he was doing."

She added: "There is something else behind all this, something bigger. What if I were the next to be killed? I am going to quit, I'll find something else to do."

Whether one serial killer or a group is responsible remains a subject of speculation. The New Times of Rwanda reported: "In most incidents eyewitnesses talk of a slender light-skinned man who appears to be in his early 30s. A man fitting that description, they say, has been sighted in areas known for sex trade in Kigali."

Local authorities have stepped up security, with awareness meetings being held and residents paying guards to patrol streets around the clock.

Badege appealed to the public to remain calm and vigilant and to co-operate with the investigation. "The government of Rwanda values every person living in Rwanda regardless of what they do," a police statement added.

The prevalence of HIV among female commercial sex workers is 51% compared with a national average of 3%, according to a 2010 national survey.