By Kim Sengupta in Camp Dogwood and Charles Glass in Suleimania, Iraq

Waves of devastating violence swept through Iraq yesterday with US forces still mired in streetfighting in their attempt to capture the rebel stronghold of Fallujah.

A suicide bombing killed at least 19 people and injured 15 in Baghdad, the explosion destroying 20 buildings and 25 cars. The northern city of Mosul was reported "out of control", with police stations stormed and masked gunmen roaming the streets. Fighting also continued in Ramadi with large parts of the city in the hands of insurgents. In Fallujah, the American military claimed to have killed more than 600 resistance fighters and to have pinned hundreds of others into a corner for a final assault. At least 18 US troops and five Iraqi government soldiers have been killed so far in Fallujah, military officials said.

Major-General Richard Natonski, commander of the 1st Marine Division, said 69 American personnel and 34 Iraqi government soldiers had been wounded since the assault began on Monday. The military had been slow in releasing official, comprehensive reports, citing security but about 225 injured soldiers are in Landstuhl Medical Centre in Germany.

The US administration and its sponsored Iraqi government had insisted the onslaught on Fallujah was justified because it had become the epicentre of insurgency in Iraq.

General Richard Myers, head of the US Joint Chiefs of Staff, declared the offensive was " very, very successful". But he also admitted: "If anybody thinks Fallujah is going to be the end of the insurgency in Iraq, that was never the objective, never our intention, and even never our hope."

The Baghdad car bomb narrowly missed its intended target, a US patrol, on Saadoun Street, in the city centre. It ripped through a packed thoroughfare, near hotels housing the capital's dwindling numbers of foreigners. Passers-by helped police pull maimed victims and dead bodies out of the rubble of buildings and wreckage of cars.

A senior police officer said the blast, which left a hole 10ft deep, was one of the worst he had seen. Ahmed Rahim Abbas, who helped ferry the injured to hospital, said: "We could feel the ground keep shaking. There were people there, old people, women, who were very badly hurt. I don't think many of them would survive."

In Mosul, militants have attacked American troops guarding bridges between the eastern and western halves of the city. Some of the rebels crossed the bridge to the eastern, Kurdish, side on Wednesday night. Sources in Mosul said they occupied a police station in the Zahour quarter, seized weapons and briefly held the police then freed them. They also set other police stations ablaze.

Mosul city authorities ordered an indefinite curfew and warned residents to stay away from the five major bridges across the Tigris river because of the fighting. Militants with rocket-propelled grenades were seen in front of the Ibn Al-Atheer hospital in the Jammia district. Captain Angela Bowman, a US spokeswoman, said some of the attacks on police stations overwhelmed "the capabilities of the existing police force" and that that five stations were ransacked.

To protect the estimated 400,000 Kurds living in Mosul, the Kurdistan Democratic Party has sent units of its Peshmerga fighters to the city. Nominally under American command within the Iraqi National Guard, the Peshmergas work under their own officers. Their arrival in Mosul threatens to plunge the Kurds into direct conflict with Iraq's Arabs and widen the war.

In Fallujah, US troops said they were steadily advancing through the city from the northern side, pushing militants slowly into the southern half. With US units to the south and east, and the Euphrates river on the west, insurgents are being squeezed into a corner, the military said.

US troops were also skirmishing with insurgents in the Wihdah and Muhandiseen neighbourhoods, said Iraqi journalist Abdul Qader Saadi. He said he had seen burnt armoured vehicles and tanks and bodies in the streets.

In another part of the city, two AH-1 Marine Cobra attack helicopters made safe landings "after being engaged by ground forces" in the Fallujah area, the US military said. American forces also found an Iraqi man chained to a wall in a building in north-eastern Fallujah. The man, shackled at the ankles and wrists, and bruised and starving, told Marines he was a taxi driver abducted 10 days ago and his captors had beaten him with cables.

Marine Captain John Griffin said: "Claiming the city is secure doesn't actually mean that all the resistance is gone; it just means we have secured the area and have control."