BAGHDAD, Iraq -- A car bomb exploded Tuesday west of Baghdad, killing at least four people a day after three dozen people died in a wave of suicide bombings in the Iraqi capital. U.S. officials said one of Baghdad's three deputy mayors was killed in a hit-and-run shooting.
The latest attacks, including the killing Sunday of deputy mayor Faris Abdul Razzaq al-Assam, raised fears that a strengthened insurgency is increasingly targeting Iraqis who work with the U.S.-led coalition as well as international groups.
In Fallujah, a flashpoint Sunni Muslim city 40 miles west of Baghdad, a car exploded Tuesday afternoon on a major street, killing at least four people.
The explosion occurred about 100 yards from a police station and 100 feet from a school, but the target was unclear.
Despite the escalation in attacks on Iraqis, American forces remained targets, with insurgents firing on a U.S. military base and convoy in two northern cities Tuesday.
In Baghdad, a rocket-propelled grenade attack killed one U.S. soldier and wounded six others while they were trying to destroy roadside bombs, the U.S. military said Tuesday.
The soldiers, from the 1st Armored Division, were attacked Monday, the same day a team of suicide car bombers devastated the Red Cross headquarters and three police stations, killing three dozen people and wounding more than 200.
In Tikrit, Saddam Hussein's hometown, insurgents opened fire late Tuesday on the southern gate of the main U.S. military base, wounding at least one American soldier from the 4th Infantry Division, witnesses said. A patrol was sent out to search for the assailants, who soldiers said apparently fired from a nearby rooftop.
And a U.S. military convoy was attacked Tuesday night by small arms fire in the northern city of Mosul, the military said. There were no casualties.
In Fallujah, a flashpoint Sunni Muslim city 40 miles west of Baghdad, a car exploded Tuesday afternoon on a major street, killing at least four people. The explosion occurred about 100 yards from a police station and 100 feet from a school, but the target was unclear.
Later Tuesday, eight huge explosions were heard after sundown from the southern area of Fallujah. U.S. officials in Baghdad said they were unaware of the blasts, which residents described as "deafening."
In Baghdad, at least three mortar shells exploded late Tuesday in the Jadriya district across the Tigris River from the palace headquarters of the U.S.-led coalition, Iraqi police said. There was no immediate word on casualties or damage.
Coalition officials reported little progress in determining who was behind Monday's car bombings in Baghdad.
A fifth would-be suicide bomber, who was caught Monday before he could detonate his explosives, told police he was Syrian, according to a coalition official. Investigators were trying to confirm his nationality, the official said on condition of anonymity.
President Bush blamed both loyalists to Saddam and foreign terrorists for the attacks in and around Baghdad, including a rocket barrage on a hotel Sunday that killed a U.S. lieutenant colonel and wounded 18 other people.
Bush told a news conference Tuesday that "basically what they're trying to do is cause people to run."
A coalition spokesman, Charles Heatly, told the British Broadcasting Corp., "there certainly are indications that there are foreign terrorists who are coming into Iraq," but he did not explicitly accuse them of responsibility.
Britain's special representative in Iraq, Sir Jeremy Greenstock, also said Tuesday that foreign terrorists could be entering Iraq from Afghanistan and elsewhere.
The use of suicide bombings in Monday's attacks "is a sign of foreign terrorist tactics, rather than the Saddam loyalist elements that we are still trying to chase down," Greenstock told BBC.
The car bombing in Fallujah was the first in the city, a center of resistance to the U.S. occupation.
Tawfiq Mijbel, who was badly wounded by shrapnel from the car bombing, said he was driving directly behind the vehicle that 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," Mijbel said from his hospital bed.
Khamis Mijbal, who owns a shop opposite the spot where the car blew up, said the blast produced a massive ball of fire and debris flew in all directions.
The school was closed, but police said one body was found inside. Police Col. Jalal Sabri said all the victims appeared to have been bystanders. Sabri said at least four people were dead but the number could reach six. The count was difficult because some victims were dismembered, he said.
The slain deputy Baghdad mayor, al-Assam, was "shot in a hit-and-run incident" Sunday, said Tom Basile, a coalition spokesman. Basile said he had no information that any suspects were apprehended.
Resistance forces have assassinated or attempted to assassinate several figures allied with the occupation. The most prominent was Aquila al-Hashimi, a member of the Governing Council, who was fatally shot Sept. 20.
Associated Press writers Tarek al-Issawi in Fallujah, Katarina Kratovac in Tkrit and Mariam Fam in Mosul contributed to this report.