The bodies of the two Chinese women were reportedly discovered at 11am in a residential building in Via Augusto Riboty, in the Prati district, while the South American was found in an apartment on nearby Via Durazzo in the same neighbourhood an hour later.

All three were “probably sex workers”, police said later on Thursday. The South American had suffered a fatal wound to the abdomen.

All three victims were stabbed and are thought to have been killed by the same person, according to Italian media reports, leading newspapers to warn of a possible “serial killer” on the loose in the capital.

The body of one of the Chinese women was spotted by a neighbour where it lay, naked on a landing. The woman, believed to be in her 40s, had suffered head and stomach injuries, the Corriere della Sera newspaper said.

When police entered her apartment, they found the body of a second Chinese woman, it said.

Nobody in the building appeared to have heard the murders take place, according to local residents.

“Everybody knew there was a house of ill repute here, I’d see people arriving at 2am, 3am,” a woman who lived in the building told reporters.

The body of the Colombian, who was 65, was found by a friend, Corriere della Sera said.

Police were examining the victims’ phone records to determine whether there was a link between them.