The attacks came just hours before Powell's visit
US President George W Bush has denounced the bomb attacks against Western targets in Saudi Arabia as "despicable acts" and vowed to bring those responsible to justice.
He was speaking amid continuing uncertainty about how many people had been killed in Monday night's apparently co-ordinated suicide bombings in the capital, Riyadh.
The Saudi authorities have put the death toll at 29 - including seven Americans and nine suspected attackers, who shot their way past armed guards and rammed vehicles packed with explosives into compounds housing mainly foreigners.
They are devoid of all Islamic and humane principles
Saudi Crown Prince Abdullah on bombers
Unidentified officials at the State Department in Washington were quoted as saying more than 90 people had been killed - but a statement later said the number of victims was nearer the Saudi estimate.
The blasts in the east of the city also injured about 200 people, according to Saudi figures, and left widespread devastation.
Mr Bush said the attacks were the work of "killers whose only faith is hatred".
His words were echoed by the Saudi Crown Prince Abdullah - the kingdom's de facto ruler - who went on national television to denounce the bombers as "criminal butchers" who were "devoid of any Islamic or human values".
The bombings came just hours before US Secretary of State Colin Powell arrived in Riyadh. But he went ahead with the visit, describing the attacks as a "cowardly operation" which bore all the hallmarks of the al-Qaeda network.
Mr Powell saw for himself the devastation at the Vinnell complex - home to US workers who train Saudi military and civilian officials - where seven Americans and a Saudi died.
One building had its side completely torn off, while the wreckage of burnt-out vehicles littered the car park.
Mr Powell told journalists that US experts would soon arrive to help the Saudi investigation into the bombings.
"Terrorism strikes everywhere and everyone," he said. "It is a threat to the civilised world."
A spokesman for UK Prime Minister Tony Blair said the developments in Saudi Arabia were being watched with "deep concern", and that Mr Blair "strongly condemned" the attacks.
And Russian President Vladimir Putin said the attacks in Saudi Arabia and Chechnya - where more than 50 died early Monday - bore the same imprint.
The attacks come two weeks after the US announced it was withdrawing most of its troops from Saudi Arabia, where they were deployed during the 1991 Gulf War.
Saudi Arabia is the birthplace of al-Qaeda leader Osama Bin Laden, who has repeatedly demanded that US forces leave the kingdom which has two of Islam's holiest shrines.
Also , 15 of the 19 men suspected of carrying out the 11 September suicide attacks on New York and Washington were Saudis.
'Shooting their way in'
The attackers - believed to be al-Qaeda members - drove cars packed with explosives at three compounds, detonating them with devastating effect.
The force of the explosion shook nearby buildings and windows, witnesses said.
Riyadh bomb victims
Source: Saudi Interior Ministry
A fourth blast was reported to have targeted the headquarters of a joint Saudi-US company, but caused no casualties.
At the Al-Hamra compound - which suffered one of the worst attacks - dozens of homes and apartments were destroyed. According to the Saudi authorities, 10 people died there, including two Jordanian children, four Saudis, two Filipinos, a Lebanese and a Swiss.
Two Saudis were also killed at the Jadwal complex in the Ishbilia area.
A number of South Asians are also feared to be among the victims.
A Sri Lankan diplomat in Riyadh, P Ranawaka, told the BBC that an injured Sri Lankan maid was in hospital and Saudi police had spoken of several casualties of South Asian origin.
American residents have been advised by the US embassy in Riyadh to stay at home and "away from windows and doors".
The attacks happened despite numerous intelligence warnings.
At talks in Riyadh, Mr Powell and the Saudi Crown Prince and the Foreign Minister, Prince Saud al-Faisal, vowed to step up co-operation against terrorism.
However the BBC's State Department correspondent Jon Leyne says that is unlikely to silence the many critics in Washington of Saudi Arabia's record in fighting terror.
Mr Powell went to Saudi Arabia as part of a Middle East tour, hoping to gain support in Riyadh for a new US-backed peace plan to end the Palestinian and Israeli unrest.