US President George W Bush has warned Iran and Syria not to let terrorists cross into Iraq from their territory.
The Falluja blast was the latest in a series of suicide attacks
"We are working closely with those countries to let them know we expect them to enforce borders," Mr Bush told journalists at the White House.
He was speaking amid an upsurge of violence in Iraq, in which dozens of people have been killed over the past 48 hours.
In the flashpoint town of Falluja on Tuesday, a suicide bomber blew up a car, killing himself and at least five civilians, witnesses said.
It came after a series of deadly co-ordinated attacks in Baghdad on Monday, when four bombs were detonated in less than an hour, killing at least 35 people and injuring more than 200.
In other attacks:
- A coalition soldier and two civilians - one of them non-Iraqi - were injured when a device exploded on a road in the southern city of Basra, where UK forces are in charge of security
- A US military convoy was attacked on Tuesday night by small arms fire in the northern city of Mosul. There were no casualties.
- A US soldier was killed and several others were wounded in a rocket-propelled grenade attack in Baghdad on Monday
American officials said Faris al-Assam, the deputy mayor of Baghdad, was shot dead in what they believe was a hit-and-run incident near his home on Sunday night
'Fear and retreat'
Referring to the spate of attacks in Iraq, Mr Bush said he assumed those responsible were "either, or - and probably both - Baathists and foreign terrorists".
He said the supporters of the ousted Baath Party "try to create chaos and fear because they realise that a free Iraq will deny them the excessive privilege they had under Saddam Hussein".
Foreign terrorists, he said, "are trying to create conditions of fear and retreat because they fear a free and peaceful state".
Mr Bush said US-led coalition forces were stepping up patrols on Iraq's borders, involving Iraqi contingents.
He drew a parallel between the suicide bombings in Iraq
and the 11 September, 2001, attacks on the United
"It's the same mentality," he said, describing the mindset of the anti-US militants as: "We'll just destroy innocent life and watch the United States and their friends and allies, you know, crater in the face of hardship".
The BBC's Rob Watson in Washington says such news conferences are rare at this White House - President Bush prefers to take a question here or there, rather than en masse.
Earlier, the chief British representative in the US-led administration, Sir Jeremy Greenstock, told the BBC 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.
The BBC's security correspondent Frank Gardner says intelligence experts believe al-Qaeda could have been involved.
The attack in Falluja took place outside a boys' school, near the main police station and a power plant in the town, about 50 kilometres (30 miles) west of Baghdad.
Classes at the school had finished for the day and the building was closed when the bomb went off, although a number of children are reported to be among the victims.
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
US troops have sealed off the area around the blast.
Eyewitness Tawfiq Mijibel was driving the car when it exploded.
"It stopped in front of the power company. A man got out while another stayed in the car. A few seconds later it blew up," he said.