"It's quite clear to me that al-Qaida wants to take down the royal family and the government of Saudi Arabia," said Armitage, who was in Riyadh to discuss the latest developments after Sunday's attack that left 17 dead.
"I can't say that last night's attack was the only or the last attack. My view is these al-Qaida terrorists - and I believe it was al-Qaida - would prefer to have many such events," he told reporters.
Earlier, US President George Bush assured Saudi Arabia that Washington stands behind Riyadh in the wake of the deadly attack.
Bush told Crown Prince Abd Allah late on Sunday that the US supported the kingdom in its “war against terrorism”, said an anonymous White House official.
Seventeen people, including five children, were killed when a double car bomb ripped through al-Muhaya residential compound west of Riyadh, according to the Saudi interior ministry.
The dead included seven Lebanese, four Egyptians, one Saudi and one Sudanese, said the ministry.
The nationalities of the remaining four fatalities had not yet been determined. About 122 people were wounded in the blast, including 36 children.
Interior Minister Prince Nayef bin Abd al-Aziz said Saudi authorities would not rest until they caught the masterminds behind the bombing.
"I can't think of an uglier crime, perpetrated against citizens and Arab Muslim residents - and even if some are not Muslim - by people who claim to be (Saudi) citizens and who claim to be Muslim,” said Nayef.
Supporters of al-Qaida group had threatened to attack Saudi Arabia's rulers and westerners in the kingdom. The group’s leader, Usama bin Ladin, last month vowed to strike American targets inside and outside the US.
Riyadh has been under pressure to act against al-Qaida and other fighters since the 11 September 2001 attacks in the US.
Saudi Arabia's ambassador to Britain, Prince Turki al-Faisal said that attacking a lightly-defended target such as the compound was a "clear sign of a desperate group that wants to show it can do things".
Rescue efforts have continued
24 hours after the deadly attacks
The blast occurred just days after Western nations issued fresh alerts and Washington shut its missions in the kingdom.
A Riyadh embassy spokesperson had refused to provide information on the nature of the threats.
On Monday security was high around diplomats and western residences across the capital.
The United States embassy was closed to the public for the
third day in a row and diplomats said it would not re-open
before Wednesday at the earliest.
A US diplomat said that Saudi officials had been responsive after Washington called for greater security.
Following the blast, the US ordered its diplomatic staff and their families in Saudi Arabia to remain in their homes and not to leave the area of Riyadh, where embassies are located.
Republican Pat Roberts, head of the Senate Select Committee on Intelligence, said that US lawmakers had received a warning one week ago that Saudi Arabia could be the target of an attack and that strikes such as the May Riyadh bombing were likely.
On 12 May, a triple suicide bomb attack targeted residential compounds in Riyadh, leaving 36 people dead.
Joseph Biden, the ranking Democrat on the Senate Foreign Relations Committee, said he hoped the attack would serve as a wake-up call for the Saudis, making them "stop building those madrassas and get serious", in reference to religious schools.
There were no details of the attackers, except that Saudi sources said there had been at least two.
Meanwhile, rescuers struggled into the night to pull bodies from the site. Teams are still searching the rubble more than 24 hours after the attack.