Authorities say two relatives of Iraqi Prime Minister Ayad Allawi have been kidnapped: a first cousin and the cousin's daughter-in-law.
An advisor to the Iraqi prime minister tells CBS News in Baghdad that six to eight kidnappers abducted the Allawi relatives as they walked out of their garage.
Police say the abductions - at first reported to involve three Allawi relatives - happened Tuesday night in the Qadisiyah section of Baghdad.
The source say Allawi is "close" to the kidnap victims and is concerned, but is carrying on with business as usual - full of "moral fibre" and determination not to give in to terrorists.
A posting on an Islamic Web site by a group calling itself Ansar al-Jihad group claims responsibility for the kidnapping and threatens to behead the victims in 48 hours if their demands aren't met.
They demanded that Allawi and his government release all female and male detainees in Iraq, and lift the siege on Fallujah.
"We promise Allah and his messenger that if the agent government doesn't respond to our demands within 48 hours, they (the hostages) will be beheaded."
The group claims to have kidnapped Allawi's cousin, the cousin's wife and another relative - a claim consistent with early reports of the crime, but one which has not been verified.
A spokesman for Allawi identifies the missing as the prime minister's cousin, Ghazi Allawi, and his cousin's daughter-in law.
"Ghazi Allawi is 75 years old. He has no political affiliation, and is not holding a government post," said Allawi spokesman Thair al-Naqeeb.
Hundreds of Iraqis have been kidnapped in recent months, mainly by groups demanding ransom.
More than 170 foreigners have been kidnapped by insurgents in Iraq since Saddam Hussein's regime fell in April 2003. More than 30 foreign hostages have been killed. Many of the kidnappers pursue political motives such as the withdrawal of foreign companies and troops from Iraq.
In Fallujah, the full-scale battle continues to wrest control of the city from rebel forces.
American forces battled through boobytrapped lanes and alleys Wednesday in a stunningly swift advance.
The military said at least 71 militants had been killed as of the beginning of the third day of intense urban combat, with the casualty figure expected to rise sharply once U.S. forces account for insurgents killed in airstrikes.
As of Tuesday night, 10 U.S. troops and two members of the Iraqi security force had been killed, a toll that already equaled the number of American troops who died when Marines besieged the city for three weeks in April.
Major Francis Piccoli, of the 1st Marine Expeditionary Force, says U.S. forces that pushed south through Fallujah's central highway overnight now control 70 percent of the city, with the remaining insurgents in a strip along the main east-west highway.
Marine reports Wednesday said 25 American troops and 16 Iraqi soldiers were wounded.
In other developments:
In Fallujah, U.S. troops were advanced more rapidly than in April, when insurgents fought a force of fewer than 2,000 Marines to a standstill in a three-week siege. It ended with the Americans handing over the city to a local force, which lost control to Islamic militants.
This time, the U.S. military has sent up to 15,000 U.S. and Iraqi troops into the battle, backed by tanks, artillery and attack aircraft.
"The enemy is fighting hard but not to the death," Lt. Gen. Thomas Metz, the multinational ground force commander in Iraq, told a Pentagon news conference relayed by video from Iraq. "There is not a sense that he is staying in particular places. He is continuing to fall back or he dies in those positions."
Metz said Iraqi soldiers searched several mosques Tuesday and found "lots of munitions and weapons."
Although capturing or killing the senior insurgent leadership is a goal of the operation, Metz said he believed the most wanted man in Iraq, Abu Musab al-Zarqawi, had escaped Fallujah.
Despite resistance being lighter than expected the top U.S. commander in Iraq said Tuesday he still expects "several more days of tough urban fighting" as insurgents fell back toward the southern end of the city, perhaps for a last stand.
"I'm surprised how quickly (resistance) broke and how quickly they ran away, a force of foreign fighters who were supposed to fight to the death," Lt. Col. Pete Newell, a battalion commander in the 1st Infantry Division, told CNN.
It is not clear how many insurgents have stayed in the city for the fight, despite months of warnings by U.S. officials and Iraqis that a confrontation was in the offing.
Metz said troops have captured a very small number of insurgent fighters and "imposed significant casualties against the enemy."
Before the major ground assault that began Monday night, the U.S. military reported 42 insurgents killed. Fallujah doctors reported 12 people dead. Since then, there has been no specific information on Iraqi death tolls.
U.S. officials said few people were attempting to flee the city, either because most civilians had already left or because they were complying with a round-the-clock curfew. A funeral procession, however, was allowed to leave.