A 57-year-old-man, understood to be Vitautas Jokubauskas, has been arrested on suspicion of murder after a woman's torso was found in a suitcase, Cambridgeshire Police said.
The man was arrested in Clipston Walk, Peterborough, at about 7pm today and is currently in custody at Thorpe Wood Police Station.
Detectives are no longer appealing for the public's help in tracing Lithuanian Jokubauskas.
The body, which had no legs arms, legs, or head, has not been identified and a post-mortem examination is due to take place tomorrow.
But detectives are still keen to trace a woman, believed to be Jokubauskas' Lithuanian partner, who is only described as being about 40, slim, and with black hair.
The torso was discovered when police attended an address in Mayor's Walk, Peterborough, just after 12.30pm on Friday.
A cordon remains in place around property while officers conduct detailed forensic investigations.
The murder is being treated as an isolated incident and a dedicated murder team has been set up to investigate.
Anyone with information should contact the Beds, Cambs and Herts Major Crime Unit on 101, or Crimestoppers, anonymously, on 0800 555111.