(Adds details, quote, background) DUBAI, June 3 (Reuters) - Saudi Arabia offered a cash reward of 5 million riyals ($1.3 million) for information leading to the arrest of sixteen people it said were involved in two deadly mosque bombings claimed by Islamic State, the Interior Ministry said on Wednesday. A suicide bomber disguised as a woman blew himself up on Friday outside a Shi'ite Muslim mosque in the city of Dammam in eastern Saudi Arabia, killing himself and four other people. A week earlier, a**ther suicide bomber blew himself up at a Shi'ite mosque in the nearby village of al-Qadeeh, killing 22 people.