BAGHDAD, Iraq - The largest Iraqi-led counterinsurgency operation since the downfall of Saddam Hussein set off a violent backlash on Sunday across Baghdad. At least 20 people were killed in the capital, 14 of them in a battle lasting several hours when insurgents launched sustained attacks on several police stations and an army barracks.

The violence, including at least four suicide car bombings, was a bloody start to an operation that Iraq's new Shiite-majority government had presented as a get-tough policy toward Sunni Arab insurgents, first in Baghdad and then countrywide. The government has said it will commit 40,000 Iraqi troops to the Baghdad operation in an effort to crush insurgents who reacted to the government's swearing-in four weeks ago with one of the war's biggest rebel upsurges.

The Baghdad toll was part of another day of bloodshed across Iraq. In total, at least 34 people were killed, including a British soldier caught by a roadside bomb near the town of Kahla that broke a protracted period of calm in the Shiite-dominated south.

A statement from the 2nd Marine Expeditionary Force said a Marine was killed Saturday when his vehicle hit a roadside bomb near Haqlaniya, bout 90 miles northwest of Baghdad.

Even before Sunday's fighting, the government of Prime Minister Ibrahim al-Jaafari appeared to have opened a new and potentially hazardous chapter in the war. Announcing the crackdown last week, government officials said the operation would move Iraqi troops "from the defensive to the offensive" in the war, and show Iraqis that the leaders they elected in January were capable of providing the security that just about every opinion poll in recent months has shown is their highest priority.

The most daring assault appeared to have been a sustained attack on the detention center run by the Interior Ministry's major crimes unit in Amariya, where suspected insurgents are held before being moved to the Abu Ghraib prison. The ministry said the assault there involved at least 50 insurgents firing rocket-propelled grenades, mortar shells and machine guns. According to an unconfirmed account by an Amariya resident who was reached by telephone, insurgent bands roaming the district after the battle claimed to have captured weapons from the detention center's armory.