Suhail Anwer Siyal, home minister for Sindh province, said the banned group had admitted being behind the attack in the city of Jacobabad, which took place on Friday outside the residence of a local Shiite leader ahead of a religious procession.
"According to initial information I have got, Lashkar-e-Jhangvi has claimed the responsibility of the blast," Siyal told local media in Karachi.
He added that the fingerprints of the suspected suicide bombers were now being analysed as police and counter-terrorism teams begin work.
LeJ are known to have been behind numerous bloody attacks on minority Shiite Muslims, who make up around 20 per cent of Pakistan's 200 million population.
In July, LeJ's leader Malik Ishaq was shot dead along with 13 other militants, including senior commanders, in Punjab, but the group remains active, according to experts.
Sindh's minister for health Jam Mehtab Dahar told AFP the death toll from the Jacobabad blast had risen to 24 from 16 on Saturday, as more wounded people succumbed to their injuries.
Regional police chief Sain Rakhio Mirani said that at least six of the victims were children.
Pakistan is on high alert and has deployed some 10,000 troops and 6,000 paramilitary members to prevent sectarian violence during the mourning days of Ashura in the holy month of Moharram, a tense period in previous years.
Moharram, which began last week, sees Shiites hold processions and gatherings to mourn the martyrdom of the Prophet Mohammed's grandson Imam Hussain at the Battle of Karbala in Iraq in 680 AD.
Hussain is equally revered by Sunnis, but hardliners oppose the public mourning of his martyrdom.
Earlier this year, another brutal attack killed 45 Shiites in Karachi. Sectarian violence has claimed thousands of lives in Pakistan over the past decade.
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