In a statement posted on a militant website, the Islamic State of Iraq said it unleashed the car bombs and other explosions to avenge the executions and "massacres" of convicted Sunni inmates held in Iraqi prisons.
It made no mention of the start of the war, but the claim of responsibility came 10 years after the U.S.-led war began on March 20 with an airstrike on Dora Farms in southern Baghdad in a failed attempt to kill Saddam.
The dictator's eventual toppling quickly led to a breakdown of law and order, enabling the rise of al-Qaida and other Sunni insurgents as well as releasing sectarian, ethnic and class hatreds that had been suppressed by his iron-fisted rule.
Most of the nearly 20 attacks on Tuesday targeted Shiite areas in Baghdad. In addition to those killed, more than 200 were wounded, officials said, demonstrating in stark terms how dangerously divided Iraq remains more than a year after American troops withdrew.
The al-Qaida statement warned the Shiite-led government to stop executing Sunni prisoners or "expect more bad events ... and seas of blood."
"What has reached you on Tuesday was the first drop of rain, and a first phase .
Violence has ebbed sharply since the peak of Sunni-Shiite fighting that pushed the country to the brink of civil war in 2006 and 2007. But insurgents are still able to stage high-profile attacks, and sectarian and ethnic rivalries remain threats to the country's long-term stability.
Iraqis showed little interest in marking the anniversary of the war that sparked years of bloodshed as Sunni and Shiite militants battled U.S. forces and each other, leaving nearly 4,500 U.S. soldiers and more than 100,000 Iraqis dead. For many Iraqis, March 20 carries less significance than April 9, the date that Baghdad fell to the Americans, forcing Saddam to flee.
"Nobody cares about this anniversary. We don't even want to remember it because it was the beginning of a tragedy that bred even more tragedies. It's a painful anniversary because it rid us of Saddam but it brought us something even worse," said Hussein Kadhim, a Shiite employee at the Oil Ministry. "The only things reminding us of the invasion are the pictures of the victims who die on a daily basis."
The symbolism of Tuesday's attacks was strong, coming 10 years to the day, Washington time, that President George W. Bush announced the start of hostilities against Iraq. It was already early March 20, 2003, in Iraq when the airstrikes began.
The violence continued Wednesday, when a car bomb exploded during rush hour in eastern Baghdad, killing two civilians and wounding four.
In the western province of Anbar, police said gunmen shot and killed Ahmed Jihad, a candidate in provincial council elections, as he was walking near his house in Fallujah city.
Medical officials in a nearby hospital confirmed the casualty figures. All spoke on condition of anonymity as they were not authorized to release information to reporters.
Associated Press writers Sameer N. Yacoub and Adam Schreck contributed to this report.