The Afghan government initially blamed the Taliban for the attacks, but the group denied responsibility. Then a spokesman for Lashkar-i-Jhangvi called a Radio Free Europe's local Mashaal station claiming that his group had carried out the bombings.
If confirmed, RFE said, it would be the Sunni extremist group's first known attack in Afghanistan.
According to the Washington Post, the group was supported in the past by Pakistan's Inter-Services Intelligence agency (ISI), though it not known whether they still have ties. Lashkar-i-Jhanvi is also believed to be linked to al-Qaeda.
If its claims are true, it marks a worrying development in Afghanistan, said the Post:
Lashkar-i-Jhangvi militants have systematically assassinated Shiites and attacked their religious gatherings in Pakistan. If the group is extending operations into Afghanistan, it could add a highly destabilizing sectarian dimension to the costly and protracted Afghan war.
It is also likely to strain further already tense relations between Kabul and Islamabad.
Visiting the casualties of Tuesday's attacks in hospital, President Karzai said Wednesday that his government had launched an investigation in to the attacks. He said he planned to involve the Pakistani government, however, since the perpetrators are believed to have come from Pakistan.
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The developments came as at least another 19 Afghan civilians were killed by a roadside bomb in the south of the country Wednesday.
The explosion occurred as a vehicle drove through the Sangin district of Helmand province, province spokesman Daoud Ahmadi told Agence France Presse.
Many of those killed belonged to the same family, with seven women and five children among the dead. Another six people were reported injured.
The latest bombing brings the number of people killed in attacks in Afghanistan to 78 in the past two days.
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