BAGHDAD, Iraq – A suicide bomber walked calmly into a popular Baghdad kebab restaurant at lunchtime yesterday and killed at least 23 people in the deadliest attack in the capital in more than six weeks.

The explosion was the bloodiest attack on a day in which a total of at least 46 people died in relentless insurgent violence across the country despite twin American- Iraqi offensives against militant smuggling routes and training centers west and north of Baghdad.

The American military announced the death of the first U.S. Marine since the operations, code-named Spear and Dagger, began Friday and Saturday respectively in Anbar province. About 1,000 American forces and Iraqi soldiers are taking part in each offensive.

Also, U.S. Marines reported killing 15 insurgents in battles near Fallujah, the Anbar province town 40 miles west of Baghdad and a perennial insurgent stronghold.

And the tribunal that will hear the case against Saddam Hussein and key members of his ousted regime released a videotape of the deposed leader’s cousin – the man known as “Chemical Ali” because of his role in the 1988 poison gas attack that killed at least 5,000 people in the Kurdish town of Halabja.

Ali Hassan al-Majid was one of eight former regime officials shown testifying before an investigative magistrate. The video recording by the Iraqi Special Tribunal had no sound, but showed Mr. Majid signing a document dated June 16.

The tribunal has set no trial dates for any former regime official including Saddam, who was shown on a video released by the panel earlier this month.

The bomber in Baghdad detonated his explosives-laden vest at the Ibn Zanbour restaurant, 400 yards from the main gate of the heavily fortified Green Zone – American and Iraqi government headquarters. The cafe was popular with Iraqi police and soldiers.

The dead included seven police officers. The bodyguards of Iraqi Finance minister Ali Abdel-Amir Allawi and 16 other police were injured, police and hospital officials said. The minister was not in the restaurant.

Secretary of State Rice predicted no quick end to the fighting.

“They’re going to continue to suffer, I’m afraid, for some time from these insurgents and terrorists who wish to just kill innocent Iraqis because they have no other alternative. But that does not mean that they are going to win the battle for Iraq,” she said yesterday on Fox TV.

Abu Musab al-Zarqawi’s Al Qaeda in Iraq claimed responsibility and said the attacker was from Qaim, near the westernmost of the two joint America-Iraqi offensives. The statement appeared on an Islamic Web site, and its authenticity couldn’t be verified.

The suicide attack was the deadliest in Baghdad since May 7, when two suicide car bombers plowed into an American security company convoy in Baghdad – killing at least 22 people.

Suicide car bombers in northern Baghdad and Saddam’s hometown of Tikrit also killed three and four people respectively.

Most of the suicide attackers are thought to belong to extremist groups such as Al Qaeda in Iraq, which has justified killing other Muslims, including women and children, in their quest to destabilize the Shiite-led government of Prime Minister al-Jaafari.

The rate of insurgent attacks has risen dramatically since Mr. Jaafari announced the makeup of his Cabinet on April 28, At least 1,142 people have been killed since that date.

Some extremists have also started threatening fellow Sunni Arabs, who make up the core of the insurgency, because some leaders of the minority Muslim sect have expressed a readiness to join the political process. Most Sunnis boycotted January’s historic election.

Sunni Arabs today were expected to name their representatives to a committee that has until mid-August to draft Iraq’s new constitution. The number of Sunni members took weeks to negotiate with the Shiite majority which now controls the government.

Despite the bloodshed, Ms. Rice expressed optimism that the political process was moving Iraq toward peace.

“Insurgencies are defeated not just militarily, they’re defeated politically. And the Iraqi people are engaged in a political process in which more and more Iraqis see their future as a political future in a united and democratic Iraq,” she said.

In three separate incidents in Fallujah, insurgents trying to place a roadside bomb opened fire with small arms and rocket propelled grenades on a group of Marines. Other insurgents attacked Marines in the same area with machine-gun fire. A suicide car bomber failed in an attempted assault. No Marines were injured and 15 gunmen were captured, Marine Captain Jeffrey Pool said. The operations are aimed at destroying militant networks near the Syrian border and north of Baghdad, the military said.