The husband of the Kenyan athlete, Agnes Tirop, has appeared in court as a suspect in her murder.
The magistrate said he would allow police to hold Ibrahim Rotich for 20 days, during which time he will be assessed to see if he is mentally fit to stand trial.
Mr Rotich was arrested last week in the coastal city of Mombasa.
Police said he was trying to flee the country.
Agnes Tirop was found stabbed to death in her home in western Kenya.
Last month she broke the world record for a women-only 10km road race, shaving 28 seconds off the previous fastest time.