Saudi clerics who have offered to mediate between militants and the government say they believe fresh terror attacks are imminent.
Saudi officials blame the attack on al-Qaeda
British officials in Saudi Arabia have warned foreigners to be vigilant after Saturday's suicide bombing in Riyadh.
The bomb at a compound housing mainly Arab workers left 17 people dead.
The Saudi Interior Minister, Prince Nayef, has denied reports that arrests were made following the attack, contradicting earlier reports.
The Saudi information ministry on Tuesday confirmed that two or three arrests had been made, but a senior Saudi official later said the authorities were not in fact sure that the three people detained had anything to do with the bombing.
Saudi Arabia's Government has ruled out any dialogue with Islamic militants.
An attack on fellow Arabs has shocked Saudis
"We can talk to them only with the gun and the sword," said Prince Nayef.
Saudi clerics who have been trying to mediate between the government and the unknown armed militants, have been unable to make a breakthrough. But the talks are said to be continuing.
Even those involved in the mediation efforts say it is unclear whether the militants are directly connected to al-Qaeda, the BBC's Paul Wood reports from Riyadh.
The US Embassy and two consulates in Saudi Arabia, which had closed on Saturday before the bombing because of warnings of an imminent attack, remain closed until further notice.
British authorities are advising against all but essential travel to Saudi Arabia.
"There's no doubt there is a continuing high terrorist threat, and there is the possibility of further serious terrorist attacks," said British Ambassador in Riyadh, Sherard Cowper-Coles.
Our correspondent reports that according to one participant in mediation efforts, the militants have made two demands:
- Immediate reform of the judicial system
- An end to "attacks on them" by the authorities.
As many as 5,000 extra police and troops, backed by armoured vehicles, have been sent to the holy city of Mecca.
Saudi officials say they believe that al-Qaeda wants to undermine the royal family's authority by scaring Ramadan pilgrims away from Islam's most holy shrine.
Saturday's bombing was the worst by suspected militants in Saudi Arabia since May, when a triple suicide attack on a housing complex in Riyadh killed 35 people.
Western embassies and residential compounds are now adding to their defences against a similar attack.