Gardai are continuing their search of the ground around the home of Ann Marie Duffin whose body was found on Monday. Detectives are looking for the sharp instrument they believe was used to kill the mother of two.
Supt John O'Connor said there is no definite line of inquiry.
The murdered woman was a native of Holland. Her children Kevin (16) and Timothy (15), are being looked after by their father, Paul, and relatives in the Tralee area.
Ms Duffin's funeral is due to take place on Monday next, and her remains will be cremated in Dublin.