One embassy official said: "Saudi authorities officially notified us on Tuesday that the group could attack again and urged foreigners to avoid travelling outside cities."
The warning was also said to have advised embassy personnel not to travel in the area where the killing occurred.
Some French residents in Riyadh said they had received text messages from their embassy informing them of the Saudi warning.
Alain Guepratte, a French embassy spokesman, said: "We have reacted immediately by informing our nationals of the warning which urged foreigners in general to be cautious and to call police as soon as they notice that they are being monitored."
Two Saudi nationals, Abdallah Sayer al-Mohammadi and Nasser bin-Latif al-Balawi, ignored an ultimatum to turn themselves in by early Wednesday.
Turki said: "They are now on the wanted list. We have to arrest them."
The men's pictures were published on the front pages of local newspapers and the interior ministry has offered $1.9m for information leading to their arrest.
Authorities said the two men had perpetrated the killings, which was the first attack on foreigners in the country since 2005.
Islamic fighters loyal to al-Qaeda launched a violent campaign to topple the US-allied Saudi monarchy in 2003, carrying out suicide bomb attacks on foreigners and government installations, including the oil industry.
Some of the 100,000 Western residents in Saudi Arabia left after the earlier attacks, reducing the number to around 60,000, but many have since returned, diplomats said.
Islamist fighters have said they want to drive "infidel" Westerners out of Saudi Arabia, the birthplace of Islam and home to its holiest sites.
Tough security measures and a major publicity campaign have helped curb the violence but diplomats say radical Islamic ideology and anger at Western policies remain strong.