Eleven of the group were Pakistanis and two were from India.
A spokesman at the al-Hussein hospital in the Shia city of Karbala, where the bodies were taken on Friday, said the five women and nine men had their hands bound and had been shot in the head.
An official, citing a report from the hospital's mortuary, said: "They were killed three days ago. Some were tortured. One body had been beheaded."
Police said the group was ambushed in a minibus heading through western Iraq from Syria, close to a well-known rest stop on the largely empty main highway across the desert, west of the city of Ramadi.
Lieutenant Moahmmed Khayoun said the group were on their way to Karbala, 80km south of Baghdad, and were ambushed by robbers who took their belongings.
Shia pilgrims have been frequent targets for attack.