JERUSALEM, June 17 (Reuters) - An Israeli tow truck driver shot and killed two Palestinians in the occupied West Bank on Sunday and told Israeli police he opened fire after they attacked him and tried to steal his vehicle.

A spokesman for Palestinian security forces, Adnan al-Damiri, said he was aware of the deaths but did not have further details because the shooting took place in an Israeli-run area out of bounds to Palestinian police under interim peace deals.

An official at the Aboul Hassan Hospital in Yatta near the West Bank town of Hebron said two Palestinian men had suffered fatal gunshot wounds, one to the head and the other to the neck.

An Israeli police spokesman said the driver told investigators he opened fire after Palestinians wielding chains and iron bars attempted to steal the truck. He was taken to an Israeli hospital for treatment and police said they were continuing to investigate.

Jewish settlers and other Israelis who travel regularly in the West Bank are licensed to carry guns.

(Reporting by Ori Lewish in Jerusalem and Ali Sawafta and Noah Browning in Ramallah, Writing by Ori Lewis, Editing by Jeffrey Heller)