TUNIS (Reuters) -A Tunisian security officer wounded in Tuesday's shooting attack outside a synagogue on the Tunisian island of Djerba has died, TAP news agency reported on Wednesday citing hospital sources, bringing the death toll to six including the shooter.

The attacker, a National Guard member, killed a colleague at a naval installation then travelled to the synagogue where an annual Jewish pilgrimage is taking place and opened fire on police and visitors before he was shot dead.

Two Jewish cousins, one French and the other Israeli-Tunisian, were killed, along with one police officer who died at the scene and another in hospital on Wednesday.

Four more police were injured, one critically, hospital sources said, along with four other visitors.

Authorities have not yet outlined a motive or said if anybody else was involved in the attack, which is the deadliest in years and took place on an island that is a major destination for Tunisia's vital tourism industry.

In 2002 an al Qaeda attack on the pilgrimage killed 21 Western tourists.

Israel's Foreign Ministry described Tuesday's attack as a "lethal shooting incident", with a spokesperson saying it was still under investigation.

The United States and France said in statements that Tunisian security forces had acted quickly to stop the attack.

(Reporting by Tarek Amara, additional reporting by Daniel Williams in Jerusalem, writing by Angus McDowall; Editing by Frank Jack Daniel, William Maclean)