The attack occurred about 7:15 a.m. near the Maitham al-Tamar shrine and just down the street from the revered Kufa mosque in the southern city. Iraq's council of ministers issued a statement giving the casualty toll and said most of the victims were Iranian pilgrims.
Tehran condemned the attack and called on the Iraqi government to bring those responsible to justice. It also blamed U.S.-led forces for failing to provide security.
Police at the scene said the suicide attacker was driving a minivan behind two buses and detonated his explosives as the pilgrims were getting off. The buses were destroyed and a mosaic-lined wall of the shrine was damaged.
Nobody claimed responsibility for the attack, but suspicion fell on Sunni extremists amid rising sectarian tensions in the country.
"The purpose is clear - to stop pilgrimage. I suspect that the criminal Baathists are behind this act," the governor of nearby Najaf, Asaad Abu Kallal, said, referring to members of Saddam Hussein's ousted party.
Radical Shiite cleric Muqtada al-Sadr also denounced the bombing. "It was meant to shake the stability in Najaf," said his aide, Sahib al-Amiri.
Kufa and its twin city Najaf, 100 miles south of Baghdad, are in a relatively peaceful area.
Iran's Foreign Ministry spokesman, Hamid Reza Asefi, called the bombing "barbaric terrorist act" and singled the Americans out for blame.
"The wrong approach of occupying Americans and their failure to be accountable in Iraq has spread violence and terrorism in this country. Terrorists, relying on America's wrong approach, continue their crimes," state-run television quoted Asefi as saying.
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The attack in Kufa also occurred a day after the U.S. military predicted an increase in vehicle bombings now that Abu Hamza al-Muhajer, also known as Abu Ayyub al-Masri, has succeeded the late Abu Musab al-Zarqawi as head of al-Qaida in Iraq. Al-Masri is an explosives expert specializing in such attacks, Maj. Gen. William Caldwell said.
The U.S. military reported 74 car bombs in the four weeks ending June 9, two days after al-Zarqawi was killed, compared with 125 in the four weeks since that date.
AP Television News footage showed the charred hulks of the buses while a bulldozer cleared the blackened mass of metal that apparently was the minivan used in the attack.
On April 6, a car bomb exploded in Najaf, killing at least 10 people some 300 yards from the Imam Ali shrine on a street that leads to the city's massive cemetery - used by Shiites from throughout the country who come to the city to bury their dead.
Pilgrims traveling to holy sites in the area also have been targeted. Other past attacks included a mortar barrage that hit the Kufa mosque in August 2004, killing 27 people and wounding 63, and a car bomb in Najaf in August 2003 that killed more than 85 people, including Shiite leader Ayatollah Mohammed Baqir al-Hakim.
Attacks on houses of worship have stoked tensions between Shiite and Sunni Muslims, especially after the Feb. 22 bombing of a Shiite shrine in Samarra, an act that triggered reprisal attacks against Sunni mosques and clerics.
The Kufa mosque holds the shrine of Muslim Bin Aqeel, a follower of Imam Hussein, the grandson of the Prophet Muhammad. It also was the site of fierce clashes between al-Sadr's followers and U.S. troops in 2004.
Millions of Shiite Muslim pilgrims from Iran and elsewhere take dangerous bus journeys through Iraq to travel to the shrines in the area. Officials have begun expanding and modernizing the now-shuttered Imam Ali Airport in Najaf in an attempt to provide safer transportation.