Initial resistance is said to be fierce. By dawn today, fighting was at close quarters and had moved at least 1 kilometer into two northern districts of the city.
Meanwhile, in and around the town of Ba'quba, northeast of Baghdad, insurgents reportedly attacked three police stations. There was also a suicide car bombing against an Iraqi National Guard base in Kirkuk.
The main ground assault into Al-Fallujah was spearheaded by U.S. Marines on the north side of the city shortly after sundown yesterday.
It began after the city's main hospital and two strategic bridges across the Euphrates River had been seized a day earlier to the west.
The first military objectives on last night were to clear explosives set up by insurgents on the roads leading into the city and then to capture a railroad station within Al-Fallujah's northern city limits.
Once the railroad station was secured, U.S. troops and their Iraqi allies continued to advance toward the city center through two northern districts, Jolan and Askari, using tanks with close support from foot soldiers.
Correspondents embedded with U.S. Marines inside the city report that, by dawn today, the coalition's advance had moved to within 1 kilometer of the city center but was proceeding slowing -- house to house, street by street.
Most of Al-Fallujah's 300,000 residents have fled the city in recent months. But there are estimates that as many as 50,000 civilians are still living within the city. The Pentagon has estimated that between 1,000 and 6,000 insurgent fighters are inside the city.
U.S. Defense Secretary Donald Rumsfeld told reporters in Washington yesterday that the battle for Al-Fallujah is expected to be a major setback for insurgent fighters. But Rumsfeld said Pentagon planners do not expect the battle to be a final showdown with the Iraqi insurgency.
"It's pretty clear that the extremists would lose a great deal [if they lost Al-Fallujah]. And I think they're quite determined to not have that happen. So suggesting anything is final -- I think it's a tough business and I think it's going to take time," Rumsfeld said.
Rumsfeld also would not confirm whether similar ground assaults are being planned against insurgents in the nearby cities of Al-Ramadi and Samarra. "First of all, these judgments and decisions, the basic decision is being made by the Iraqi government," he said. "They then discuss it with the coalition forces. And if we agree, we assist in ways we can assist. So the answer should come from the Iraqi government to a question like that. Second, even if we were planning to go to the cities you mentioned [Al-Ramadi and Samarra], we wouldn't talk about it."
Elsewhere in Iraqi, militants stormed police stations near the Iraqi town of Ba'quba, northeast of Baghdad. Iraqi General Walid al-Azzawi said four of the assailants were killed. There were conflicting reports on the number of others that may have been killed.
It was the third series of attacks on Iraqi police stations by insurgent fighters in as many days.
There also was a suicide bomb attack on a National Guard base near Kirkuk, killing three people.
(compiled from agency reports)[For the latest news on Iraq, see RFE/RL's webpage on "The New Iraq".]