U.S. allies Poland, Japan and Bulgaria rejected the threats of new attacks by militants if they don't pull their troops out of Iraq.
Separately, a terrorist group said it had kidnapped men from India, Kenya and Egypt, and threatened to kill them if those countries did not pull their troops out of Iraq. Those countries have no troops in Iraq.
The car bomb went off in the eastern part of Baghdad, a health official said. Associated Press Television News footage showed at least three corpses covered in sheets, including one body that had been dismembered by the blast.
The U.S. soldier was on patrol in a Bradley fighting vehicle in Duluiyah, 45 miles north of Baghdad, when a bomb detonated shortly after midnight, said Maj. Neal O'Brien of the 1st Infantry Division.
In other developments:
"We are keen to ask for Arab support, including that of Egypt, which faced hard times with terrorism," said Iraqi interim Prime Minister Iyad Allawi, who flew into Cairo Wednesday as part of a tour of several Arab states. "Iraq is part of this region and all the countries are now passing through difficult times."
Iraqi Foreign Minister Hoshyar Zebari on Tuesday said Iraq's neighbors can't continue to only support his country verbally. He appealed for practical steps to root out international terrorism, including the creation of bilateral security committees.
"We expect some of our neighbors to stand by the Iraqi people, to help us in deeds and not words, and to support the effort of the new Iraqi sovereign government to establish a peaceful, responsible Iraq friendly to its neighbors. And this is what we have come to ask them for," Zebari told reporters Wednesday.
A Turkish diplomat told The Associated Press that several proposals were being discussed Wednesday, including a proposal to hold regular meetings of law enforcement officials from countries in the region.
The diplomat, speaking on condition of anonymity, said Iraqi officials acknowledged during the closed-door meeting that infiltrations both out of and into Iraq were of regional concern. The diplomat did not elaborate.
The terrorist threats to foreign troops came a day after militants released Filipino hostage Angelo dela Cruz after his country gave in to their demand and pulled its 51-member force out of Iraq.
Iraqi and U.S. officials have expressed concerns that the Philippines pullout would embolden militants to take more hostages in an effort to drive a wedge between coalition countries and force trucking companies and other contractors to leave Iraq.
More than 60 foreigners have been taken hostage in Iraq in recent months.
The same group that kidnapped dela Cruz, the Khaled bin al-Waleed Corps, took aim at Japan. In the posting, the group said it was the military wing of Tawhid and Jihad, led by Jordanian militant Abu Musab al-Zarqawi.
"To the government of Japan: Do what the Philippines has done. By God, nobody will protect you and we are not going to tolerate anybody," said a statement signed by the group. "Lines of cars laden with explosives are awaiting you; we will not stop, God willing."
A Foreign Ministry official in Japan said Wednesday that Tokyo would not pull its 500 troops, sent here for medical and reconstruction duty. Japan refused in April to withdraw after three Japanese were kidnapped by Iraqi insurgents. They were released unharmed.
Likewise, Bulgarian President Georgi Parvanov said his country "will not give in to the terrorists' pressure. We will resist."
Meeting the demands to pull out Bulgaria's 480-member infantry battalion would encourage more terrorist acts, Parvanov said on a trip to Berlin.
In Warsaw, Prime Minister Marek Belka said Poland would not consider bringing home its 2,400 troops from Iraq in light of the new threat.
"The decision by the Philippines government only increases the danger for others," Belka said. "It is a very clear example of how when you bow in to the pressure of terrorists you increase the danger to others."
In other violence, a member of Baghdad's provincial council, Sabeeh al-Ka'abi, was injured in an assassination attempt. A roadside bomb hit an Iraqi police patrol in Kirkuk in the country's north, killing one policeman and injuring another. And the chief of the police force that guards the electricity infrastructure in Diyala Province, was wounded along with three other police in a roadside bomb attack.