Obama met the Custodian of the Two Holy Mosques, King Salman bin Abdulaziz of Saudi Arabia, in the White House.
Five others killed in the fire at Saudi Aramco residential complex are yet to be identified.
Around 200 women had expressed interest in running as candidates in the December 12 municipal elections.
National oil company Saudi Aramco said the fire broke out in a basement of the Radium residential compound.
Unidentified gunmen opened fire on a patrol in Jeddah before escaping in their vehicle.
A border post in the Kingdom's Jazan region came under attack on Saturday, prompting guards to respond to the fire