After Sunday's commando raid freeing dozens of foreign hostages held by suspected al-Qaida members, Saudi security forces intensified their efforts and set up nationwide checkpoints.
A manhunt was launched to root out three of four hostage takers who had managed to escape the commando raid.
A Saudi Interior Ministry statement said one of the three was wounded.
The leader of the hostage takers, Nimr al-Baqmi, was captured during the rescue of men, women and children from the residential compound.
Twenty-two civilians, 19 foreigners and three Saudis were killed in the raid.
In an effort to calm international alarm at worsening security, state oil giant Saudi Aramco vowed to keep its crude supplies flowing smoothly to avert a rise in already-high world oil prices.
Senior Saudi oil officials also met top Western oil executives in Dhahran to reassure them about security.
An oil executive said he did not expect an exodus of expatriate workers.
The Khobar assault was the second in less than a month on the Saudi oil industry, a lifeline of the world economy.