Three members of Iraqi PM Iyad Allawi's family have been abducted, an interim government spokesman says.
The abductions may be revenge for Allawi's support of the Falluja attack
Mr Allawi's first cousin, the cousin's wife and their daughter-in-law were kidnapped from their Baghdad home on Tuesday, spokesman Georges Sada said.
They were seized in the south-western Qadisiyah district after a gun-battle, police told Reuters news agency.
An Islamic group has said it is holding the three, and threatened to kill them unless the assault on Falluja stops.
The threat was issued in a posting on an Islamic website by a group calling itself Ansar al-Jihad.
The group also wants prisoners held by Iraqi and US forces freed. It says the hostages will be killed within 48 hours unless its demands are met.
The BBC's Caroline Hawley in Baghdad said the abduction of Mr Allawi's relatives seems to have been the closest insurgents could possibly have got to him.
The interim prime minister gets death threats every day and it is extremely difficult to get anywhere near him, such is his security, our correspondent says.
Criminal gangs are believed to be behind a wave of abductions of hundreds of Iraqi citizens in recent months.
Aid worker held
Most are released after a payment of ransom.
Foreigners have also been seized, with many handed over to Islamic militant groups.
Hassan was seized by an unknown group in Baghdad on 19 October
More than 30 foreign hostages have been killed, several by beheading, after kidnappers' demands were not met.
Among those currently held captive is aid worker Margaret Hassan, who has Irish, British and Iraqi nationality.
In a video released last week, her abductors threatened to hand her over to militant Abu Musab al-Zarqawi unless British troops quit Iraq.
However, a later message posted on an Islamic website claiming to come from Zarqawi's group called for Mrs Hassan's release.
The Jordanian-born Zarqawi has admitted beheading several foreigners, including Briton Ken Bigley.