American warplanes and armored vehicles have been taking aim at Fallujah, in what residents call the most intense shelling in weeks. The military says the purpose is to "restore security and stability."
The city's general hospital says at least five people have been killed.
The offensive comes as a Fallujah delegation pulled out of peace talks with the Iraqi government, saying a demand to hand over terror leader Abu Musab al-Zarqawi was "impossible."
Iraq's prime minister warned yesterday that the city would face an attack if it didn't hand over al-Zarqawi. A city spokesman says it has exhausted all peaceful solutions and is now "ready to bear arms."
Earlier, insurgents struck deep inside Baghdad's heavily fortified Green Zone, setting off bombs at a market and a popular cafe that killed at least 10 people including four Americans and wounded 20 others in the compound housing foreign embassies and Iraqi government offices.
In other developments:
The attack in the Baghdad Green Zone was the first time bombers had gotten inside the 4-square-mile compound — surrounded by concrete walls, razor wire, sandbag bunkers and guard posts — and was the deadliest attack within the area since the U.S. occupation began in May 2003.
The U.S.-guarded enclave — home to about 10,000 Iraqis, government officials, foreign diplomats and military personnel — spreads along the banks of the Tigris River in the heart of the capital. The area's trees and other greenery present a sharp contrast to the rest of dusty and arid Baghdad. The zone is centered on Saddam Hussein's mammoth Republican Palace, and there are dozens of smaller palatial buildings, houses, office buildings and a hospital once used by high-ranking members of the old Baath Party regime.
The bombings, which underscored that no part of Baghdad is truly safe, took place about 12:40 p.m. on the eve of the Islamic holy month, Ramadan. Last year, the start of Ramadan was marked by a major escalation of insurgent violence.
Across the Tigris River, two U.S. soldiers were killed Thursday in eastern Baghdad — one when his patrol came under small arms fire, the other in a roadside bombing — the U.S. command said. Two more American soldiers were killed when their Humvee was struck by a rocket-propelled grenade and caught fire during a raid in Ramadi, 70 miles (112 kilometers) west of the capital, the military said.
Iraqi National Security Adviser Qassem Dawoud said the Green Zone attacks appeared to be a "suicide operation" — as was claimed in the Web site statement.
"This cowardly act will not go unpunished," Dawoud said. "We will strike them wherever they are."
A waiter and restaurant patrons saw two men enter the Green Zone Cafe clutching large bags. One appeared nervous while the other seemed to be trying to reassure him, they said.
The two men ordered tea and talked for about 20 minutes — a waiter thought they spoke with Jordanian accents. The more confident of the two then walked out and hailed a taxi, the witnesses said. Minutes later a loud explosion rocked the compound.
"It was then that the second bomber blew himself up," said one Iraqi vendor, afraid to give his name. "I fell on the floor, then quickly gathered myself and ran for my life."
The blast left a gaping crater in the pavement where the canopied restaurant once stood. Splatters of blood and pieces of flesh were scattered among the twisted metal, shards of glass and upended plastic chairs littering the scene. Thick, black smoke billowed from the compound.
"People were screaming ... stampeding, trying to get out, " said Mohammed al-Obeidi, the owner of a nearby restaurant who was wounded by flying glass from the cafe blast.
Six Iraqis were killed at the cafe and several U.S. Embassy employees suffered minor injuries there, State Department spokesman Richard Boucher said in Washington.
Four American employees of DynCorp security company were killed and two State Department employees were wounded in the blast in a vendor's alley near the U.S. Embassy annex. The outdoor bazaar that caters to Westerners, selling everything from mobile phone accessories to pornographic DVDs.
The Green Zone is a regular target of insurgents. Mortar rounds are frequently fired at the compound, and there have also been a number of deadly car bombings at its gates. Last week a bomb was found in front of the Green Zone Cafe but did not explode.
Al-Obeidi, the restaurant owner, said security in the zone has weakened since Iraqi police took a greater role with the June handover of power.
"Before it was really safe. They (the Americans) passed it over to the Iraqis ... the Iraqi Police. When they see someone they know, it's just, 'Go on in.' They don't understand it's for our safety," al-Obeidi said.
Following Thursday's attack, the U.S. military said intelligence reports indicated insurgents were planning more strikes to "gain media attention."
Security measures in the capital and surrounding areas would be "significantly increased for an undetermined period," a military statement said. They include more armed patrols, intensified security at Baghdad airport and elsewhere, and air patrols.
U.S. Embassy personnel were instructed to remain inside the embassy complex until further notice, Boucher said. The U.S. Embassy also "strongly encouraged" Americans living or working in the Green Zone to limit their movements, travel in groups and avoid restaurants