The attack occurred about 7.15am near the shrine of Maitham Al Tamar, a follower of Imam Ali, and just down the street from the revered Kufa mosque.
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 for it to justice. It also blamed US-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 Hussain's ousted party.
Kufa and its twin city Najaf, 160km south of Baghdad, are in a relatively peaceful area.
"We denounce this act targeting innocent people and pilgrims," an aide to radical cleric Moqtada Al Sadr, Sahib Al Amiri, said.
"It was meant to shake the stability in Najaf." Iran's Foreign Ministry spokesman, Hamid Reza Asefi, called the bombing "barbaric terrorist act" and blamed US-led forces in Iraq for failing to provide security in Iraq.
"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.
The attack came as Iraqi Prime Minister Nouri Al Maliki returned to Iraq after a regional tour to drum up support for his 24-point national reconciliation plan.
The Shiite leader on Wednesday demanded an independent inquiry of the rape-slaying of an Iraqi girl and the killing of her family, as well as a review of the immunity rules protecting US forces.
Al Maliki, whose brief tenure has been marked by several high-profile allegations of abuse by US forces, called for an Iraqi investigation or at least a joint inquiry into the March 12 rape-murder of Abeer Qasem Hamza, and the killing of her mother, father and sister at their home in Mahmoudiya, south of Baghdad.
"We believe that the immunity given to members of coalition forces encouraged them to commit such crimes in cold blood [and] that makes it necessary to review it," Al Maliki told reporters in Kuwait, calling for the policies to be reviewed.
Former Army Pfc. Steve D. Green was charged on Monday in federal court in Charlotte, North Carolina, with rape and four counts of murder. Green was held without bond. At least four other US soldiers still in Iraq are under investigation in the attack.Güncelleme Tarihi: 20 Eylül 2018, 18:16