A spokesman for the prime minister, Georges Sada, said Allawi's first cousin was abducted by masked militants outside of his home in southwestern Baghdad. The cousin's wife and daughter-in-law also were taken as hostages.
The militant group Ansar al-Jihad purportedly has issued a statement on an Islamist website claiming responsibility for the abductions. It says the hostages will be beheaded in 48 hours unless the Allawi orders an end to the Al-Fallujah assault and the release of insurgent prisoners. The authenticity of the statement could not be immediately verified.
But Muna Ali, a member of the central leadership of Allawi's Iraqi National Accord, said the kidnapping was clearly politically motivated. She made the comments today in an interview at RFE/RL headquarters in the Czech capital Prague.
"This is certainly political pressure for many reasons -- such as to try to stop the operations in Al-Fallujah or as an expression of [opposition] to the elections, or other things. I think that to submit to terrorists would be a political failure. And I don't that that is going to happen."
Ali explained that none of the hostages play a political role in Iraq. She said they were kidnapped for no other reason than being relatives of the interim prime minister.
"Regarding the security situation, security is bad outside of the Green Zone," Ali said. "But Dr. Iyad Allawi and other Iraqi officials are protected by the multinational forces and the American forces that are currently in Iraq. I don't think [it is possible] to protect every member of Allawi's family."
Some 15,000 U.S. soldiers and allied Iraqi government troops launched a ground assault on Al-Fallujah on 8 November. U.S. military officials today said they had seized positions in 70 percent of the city. Embedded correspondents report that the insurgents continue to put up stiff resistance.
U.S. tanks came under heavy fire today from militants with assault rifles and rocket-propelled grenade launchers as they attempted to move from a northern residential district to take control of Highway 10, which divides Al-Fallujah into its northern and southern halves. By noon, the U.S. Marines were claiming control of most of the highway.
By mid-afternoon, the heaviest fighting appeared to be focused in the eastern and southeastern parts of the encircled city. Analysts said some of the insurgents might be trying to slip out of the city from the southeastern side.
At the Pentagon yesterday, U.S. Army Lieutenant General Thomas Metz told reporters that the fight for Al-Fallujah could last for several more days.
Metz also said the Pentagon now believes Jordanian-born militant Abu Mus'ab Zarqawi - viewed by the U.S. as a leader of the insurgency -- fled Al-Fallujah before the ground assault began: "From a tactical point of view, I'm making an assumption that Zarqawi has left [Al-Fallujah]. I still have the [intelligence] capability to hunt him in the city as we fight. But because we think he moves around Iraq, we are keeping the [intelligence] capability looking for him outside of Fallujah also."
At the start of the offensive, American officers estimated there were up to 6,000 insurgents in Al-Fallujah. About 80 percent were thought to be Iraqis and the rest foreigners like Zarqawi.
According to the latest assessment from the Pentagon, some 2,000 to 3,000 insurgents have been fighting against the U.S.-led assault.