U.S. and Iraqi troops pushed deeper into Fallujah, battling through booby-trapped lanes and alleys today (Wednesday) in their operation to retake the city from insugents.

News reports cited U.S. military officers in the area as saying coalition troops now control almost 70 percent of the city. The officers say there are still several pockets of resistance.

A senior U.S. commander (Lieutenant General Thomas Metz) said Tuesday coalition forces destroyed the insurgents' outer ring of resistance during the first two days of the assault, but tough urban fighting days were still ahead.

He said the most wanted man in Iraq, terrorist leader Abu Musab al-Zarqawi, likely fled the city before the assault.

The U.S. military said 10 American troops and two Iraq soldiers have been killed since the operation began Monday.

The military said insurgent casualties were higher than expected, but it did not provide figures.

Most of Fallujah's residents fled before the offensive.

Two relatives of Iraqi interim Prime Minister Iyad Allawi have been kidnapped in Baghdad.

The prime minister's spokesman says Mr. Allawi's cousin, 75-year-old Ghazi Allawi, and Ghazi's daughter-in-law were seized Tuesday evening. He said the elder Allawi has no connection with any political party.

A previously unknown group (Ansar al-Jihad) has claimed responsibility for the abductions and has threatened to behead the two hostages in 48 hours unless the assault on Fallujah ends and all Iraqi prisoners are released.

Meanwhile, clashes between authorities and gunmen have been reported in parts of the northern city of Mosul (Wednesday).

Elsewhere, the U.S. military says an American soldier was killed and another wounded in a roadside bomb blast in Balad, north of Baghdad.

Further north (near Tuz), roadside bombs killed six Iraqi soldiers.