In an interview with CNN, First Lieutenant Lyle Gilbert, a spokesman for the 1st Marine Expeditionary Force, said two battalions of U.S. Marines have attacked rebel positions in the city to "restore security and stability."
Gilbert would not say if any U.S. forces have entered Al-Fallujah, but he called it a major operation. The AFP news agency says some 1,000 U.S. and Iraqi ground troops are moving toward the city, 65 kilometers west of Baghdad.
A U.S. military statement said "this operation puts the anti-Iraqi forces in Fallujah on notice."
U.S. war planes struck overnight at sites in the city the United States said were being used by senior al-Zarqawi associates as planning centers for terrorist operations.
But one Al-Fallujah resident said the airstrikes did not appear to be so precise. "Last night, there was random bombing. A family tried to get out during the bombing with their car, but they were hit twice," the resident said.
A doctor at Al-Fallujah General Hospital said three people were killed overnight. The hospital said at least five people were killed yesterday.
News agencies say talks between the Iraqi government and Al-Fallujah officials broke down yesterday. The talks came after Iraqi interim Prime Minister Ayad Allawi warned that Al-Fallujah must surrender al-Zarqawi or face military attack. But city representatives complained that handing over al-Zarqawi is an "impossible condition."
Al-Zarqawi's Jama'at Al-Tawhid wa Al-Jihad group claimed responsibility for yesterday's deadly twin bombings inside Baghdad's heavily guarded Green Zone. The enclave is home to about 10,000 Iraqis, government officials, foreign diplomats, and military personnel. The attacks killed at least five people, including three Americans.
A spokesman for the U.S. State Department, Richard Boucher, condemned the bombings.
"There's an effort that we are making to try to help the Iraqi people rebuild their country, and it's another example of where there are terrorists who want to attack the Iraqis, who want to attack us and want to attack anybody who's trying to establish opportunity and freedom for the Iraqi people. We know that's the situation there," Boucher said.
Iraqi National Security Adviser Qassim Dawud vowed to hunt down those responsible.
"This cowardly act will not go unpunished, and I would like to send a message to the terrorists, and to terror in all its forms -- the terror led by al-Zarqawi and Al-Qaeda, or the terror led by elements of Saddam Hussein's regime -- that we will defeat them," Dawud said. "We will strike them wherever they are."
Last year, the Muslim holy month of Ramadan coincided with a wave of violence in Iraq. But one Baghdad resident said he hopes things will be different this year. "We do not want fighting in this month," the resident said. We hope that the government will calm things down because fighting is forbidden in this month."
But Iraq's Interior Ministry reports that at least one civilian was killed and at least nine Iraqi policemen were wounded in a car bombing today in a Baghdad suburb.
(RFE/RL/international news agencies/CNN)