NEAR FALLUJAH, Iraq - U.S. Army and Marine units thrust through the center of the insurgent stronghold of Fallujah today, fighting bands of guerrillas in the streets and conducting house-to-house searches on the second day of a major offensive to retake the city from Islamic militants.

A total of 14 Americans have been killed in the past two days across Iraq - including five in and around Fallujah and nine others killed as guerrillas launched a wave of attacks in Baghdad and elsewhere.

A senior Pentagon official said today the nine were killed Monday southwest of Fallujah and in the capital.

Prime Minister Ayad Allawi today declared a nighttime curfew in Baghdad and its surroundings - the first curfew in the capital for a year - a day after a string of insurgent attacks in the city killed nine Iraqis and wounded more than 80.

Hundreds of guerrillas were swarming the streets of Ramadi, another insurgent stronghold 70 miles west of Baghdad where Allawi declared a curfew on Monday. Gunfire rang out in the city center, and a destroyed car smeared with blood was seen.

Allawi called on Sunni Muslim fighters in Fallujah to lay down their weapons to spare the city and allow government forces to take control, saying, "The political solution is possible even if military operations are ongoing," his spokesman said.

The U.S. military reported lighter-than-expected resistance in Jolan, a Sunni-militant held warren of alleyways in northeastern Fallujah where the assault began.

But heavy street clashes were raging in other northern sectors of Fallujah amid fierce bursts of gunfire, residents said. At least two American tanks were engulfed in flames, witnesses said. There was no confirmation of casualties.

A Kiowa helicopter flying over southeast Fallujah took groundfire today, injuring the pilot, but he managed to return to the U.S. base. By midday, U.S. armored units had made their way to the central highway in the heart of the city, crossing over into the southern part of Fallujah, a major milestone.

The once constant thunder of artillery barrages has been halted with so many troops moving inside the city's narrow alleys. U.S. and Iraqi forces have surrounded a mosque inside the city that was used as an arms depot and insurgent meeting point, the BBC reported.

Col. Michael Formica, commander of the 1st Cavalry Division's 2nd Brigade, said today that a security cordon around the city will be tightened to insure insurgents dressed in civilian clothing don't slip out.

"My concern now is only one - not to allow any enemy to escape. As we tighten the noose around him, he will move to escape to fight another day. I do not want these guys to get out of here. I want them killed or captured as they flee," he said.

Overnight the skies over Fallujah lit up with flashes of air and artillery barrages as American forces laid siege to the city that had become the major sanctuary for Islamic extremists who fought Marines to a standstill last April.

A U.S. military spokesman estimated that 42 insurgents were killed across the city in bombardment and skirmishes before the main assault began Monday. Two Marines were killed when their bulldozer flipped over into the Euphrates near Fallujah.The initial ground assault into Fallujah's northeastern Askari neighborhood and Jolan neighborhood was made by U.S. Army tanks and Humvees. U.S. Marines went up to the edge of the city, secured the area and then armored vehicles crushed the barriers and pushed into the city, with the Marines following.This reporter, located at a U.S. camp near the city, saw orange explosions lighting up the district's palm trees, minarets and dusty roofs, and a fire burning on the city's edge.A U.S. jet fired an air-to-ground missile at a building late Monday from which U.S. and Iraqi forces had taken fire, the U.S. command said. The building was destroyed.U.S. troops cut off electricity to the city, and most private generators were not working - either because their owners wanted to conserve fuel or the wires had been damaged by explosions.Residents said they were without running water and were worried about food shortages because most shops in the city have been closed for the past two days.By nightfall, a civilian living in the center of Fallujah said hundreds of houses had been destroyed.The top U.S. commander in Iraq, Gen. George Casey, told reporters in Washington that 10,000 to 15,000 U.S. troops, along with a smaller number of Iraqi forces, were encircling the city. The offensive is considered the most important military effort to re-establish government control over Sunni strongholds west of Baghdad before elections in January."There aren't going to be large numbers of civilians killed and certainly not by U.S. forces," said Defense Secretary Donald Rumsfeld.On Monday, a doctor at a clinic in Fallujah, Mohammed Amer, reported 12 people were killed. Seventeen others, including a 5-year-old girl and a 10-year-old boy, were wounded, he said.About 3,000 insurgents were barricaded in Fallujah, U.S. commanders have estimated. Casey said some insurgents slipped away but others "have moved in." U.S. military officials believe 20 percent of Fallujah's fighters are foreigners, who are believed to be followers of Jordanian militant Abu Musab al-Zarqawi.Casey said 50 to 70 percent of the city's 200,000 residents have fled. The numbers are in dispute, however, with some putting the population at 300,000. Residents said about half that number left in October, but many drifted back.In Britain, Iraq's deputy prime minister on Tuesday defended the controversial operation, saying that the overwhelming majority of Iraqis wanted order to be restored to the insurgent stronghold."The terrorists are mindless, they are killing our children and trying to destroy our lives and take us back to tyranny," Barham Saleh, who is responsible for national security, told British Broadcasting Corp. radio. "The overwhelming majority of the Iraqi people want this situation to end."