Britain has revised its travel advice for Saudi Arabia to highlight "credible" reports of planned attacks, including against Westerners.
King Abdullah took over as monarch after his brother King Fahd died
A notice on the Foreign Office website warns of the continuing "high threat" of terrorism, with "aviation interests" remaining a possible target.
Non-essential staff and dependants at UK missions in the country have been told to leave if they wish, it adds.
Saudi forces are also maintaining levels of enhanced security.
The move comes after the American Embassy shut its missions in Saudi Arabia until Wednesday due to threats against US government buildings in the kingdom.
The warning was the second in two weeks - on 25 July, the US embassy said militants were probably planning new attacks in the country.
Australia's Department of Foreign Affairs and Trade has also warned Australians not to travel to Saudi Arabia, while its nationals were urged to depart or exercise extreme caution.
Saudi Arabia has been ruled since its foundation by the Al Saud dynasty. King Abdullah succeeded the late King Fahd, his half brother, in August 2005.
As crown prince, Abdullah had been the effective ruler of Saudi Arabia since the former king suffered a stroke in the mid-1990s
Islamic militants have carried out numerous bombings in the last two years in Saudi Arabia, including on Western housing compounds, as well as kidnappings.
The Foreign Office website says Saudi security forces have had "notable success" in disrupting some terrorist operations.
But it warns: "This continuing success should not give rise to complacency. As terrorist networks are disrupted, there are grounds for believing that remaining terrorists may resort to opportunistic attacks on Western targets."
'High threat of terrorism'
Individuals who choose to travel to, or remain in, Saudi Arabia should take "all necessary steps" to protect their safety and maintain a "high level" of vigilance, particularly in public places, the warning adds.
"There are credible reports that terrorists are planning further attacks in the near future. There is a continuing high threat of terrorism in Saudi Arabia," it says.
"We continue to believe that terrorists are planning further attacks, including against Westerners and places associated with Westerners in Saudi Arabia."