At the same time, the US embassy has restricted the movement of its diplomats to mission bases and urged Americans to leave the kingdom.
There was no immediate indication if the latest attack would prompt an exodus by the 35,000 Americans living in Saudi Arabia - a move that could badly damage the economy of the world's biggest oil exporter.
Saudi Arabia has been battling a year-long campaign by insurgents suspected of links to Saudi-born Usama bin Ladin's al-Qaida network.
Saturday's attack, the first against a vital economic facility, suggested militants were determined to act on threats to destabilise the kingdom and force Westerners out.
Two Americans, two Britons and an Australian were killed in the shooting. The body of one victim was dragged by car through the streets of the Red Sea industrial city.
Yanbu residents said two bearded gunmen dressed in Western clothing dragged the corpse past two local schools and residential areas, firing into the air to attract attention and yelling "God is greatest".
Security sources said the attackers were two sets of brothers from the same family - Sami, Samir, Ayman and Hani al-Ansari.
The US embassy told staff to keep a low profile and urged other Americans to do the same while also reminding them of advice last month that they should leave the Gulf state.
"The US mission in Saudi Arabia wishes to advise the American community that until further notice, mission American employees will limit their movements off the diplomatic quarter in Riyadh and the consulate compounds in Jidda and Dhahran to essential activities only," it said.
The Westerners killed on Saturday included the top three officials at an upgrade project being carried out by Swiss-based firm ABB Lummus at the Saudi petrochemical firm Yanpet, jointly owned by US ExxonMobil and Saudi Basic Industries Corp (SABIC).
ABB Lummus said all 90 of its expatriate staff and about 30 dependents were being evacuated from Yanbu.
"Given the choice of staying under tighter security or leaving, they opted for leaving," spokesman Bjorn Edlund said.
Other expatriates in the city said it was too soon to decide.
"It's been a shock," said one. "There's been no panic but everyone is concerned and they will have to decide what steps to take."
Saudi police beefed up security in the city, home to a large foreign business community, erecting checkpoints and roadblocks, after Saturday's attack.
The four gunmen were later killed in clashes with police. Two officers also died and 18 were injured.
Crown Prince Abd Allah said "foreign elements" were behind the attack. The Saudi ambassador to Britain said it was al-Qaida.