There is increasing evidence that foreign fighters are involved in the attacks against Western targets in Iraq, the US and UK have said.
Most of those killed and injured were Iraqis
The use of suicide bombers in Monday's devastating series of attacks in Baghdad was a tactic associated with "foreign elements", said the chief British representative in the US-led administration, Jeremy Greenstock.
At least 35 people were killed and more than 200 injured in bombs at the headquarters of the International Committee of the Red Cross (ICRC) and three Iraqi police stations.
The BBC's Security Correspondent Frank Gardner says intelligence experts believe al-Qaeda could have been involved.
But he says the question of foreign involvement in the attacks in Iraq is murky and so far inconclusive.
The dead included eight Iraqi policemen, at least 26 Iraqi civilians and a US soldier.
A car bomb attack at a fourth police station was foiled. US military officials said the captured would-be bomber told police he was Syrian and was found to be carrying a Syrian passport.
Click here to see where the bombings happened
Mr Greenstock said the style of the attacks on Monday indicated non-Iraqi fighters were involved.
"There were suicide attackers in most - probably all - the bomb explosions... and that is a sign of foreign terrorist tactics, rather than the Saddam loyalist elements that we're still trying to chase down," he told BBC Radio 4's Today programme.
"I think that Iraqis are beginning to get quite angry that foreigners have come in and started to follow a war on their soil against their interests."
US Brigadier General Mark Hertling said Monday's attacks bore the hallmarks of "foreign fighters".
But a senior US commander in northern Iraq, Major General Raymond Odierno, said virtually all the fighters opposing his troops were Iraqis.
"We have not seen a large influx of foreign fighters thus far," he said.
MAJOR BOMB ATTACKS
26 October: Rocket attack on Baghdad's Rashid Hotel kills one, injures 17
12 October: Suicide car bomb outside Baghdad Hotel - six killed
9 October: Suicide car bomb hits police station in the northeast Shia district Sadr City - at least 10 killed
29 August: Car bomb at mosque near Najaf - 125 killed including Shia Islam top cleric
19 August: UN headquarters, Baghdad - 23 killed, including Sergio Vieira de Mello, veteran official
7 August: Jordanian Embassy - at least 14 killed
The ICRC has said it is reviewing its operations in Iraq after the attack on its building, which killed at least 12 people.
US Secretary of State Colin Powell has urged aid agencies to stay in Baghdad, saying withdrawal would be a victory for terrorists.
Monday was the bloodiest day in Baghdad since Saddam Hussein's regime fell to US-led forces in April.
The attacks came within less than two hours. The bomb which hit the Red Cross building appears to have been packed into an ambulance, which exploded as it entered the gates.
It was the first time a suicide bomber had struck the famously neutral ICRC in its 140-year history, and after two decades of humanitarian work in Iraq.
Many aid agencies scaled back their work in Iraq following an attack on the United Nations headquarters in Baghdad in August that killed 23 people including the top UN envoy to Iraq, Sergio Vieira de Mello.