A spokesman for President Hamid Karzai said the government plans to meet with Pakistan over the claims by an offshoot of Lashkar-e-Jhangvi, CNN reported.
At least 60 people were killed and more than 200 were injured Tuesday in explosions near shrines in Kabul and Mazar-e Sharif.
A man identifying himself as a spokesman for Lashkar-e-Janghvi al-Almi, a group with links to al-Qaida and the Pakistan Taliban, made the claim in a call to a Pakistan radio station.
The Wall Street Journal said the attacks were the first against Afghan Shiites since the Taliban regime was ousted in 2001.
"This is new," Kate Clark, a senior analyst at the Kabul think tank Afghanistan Analysts Network, told the Journal. "It doesn't fit into anyone's traditional mode of operation."
Afghan Shiites mostly belong to the Hazara community whose members were severely persecuted in the 1990s by the Taliban, the report said.
The Taliban in Afghanistan denied involvement and denounced the attacks as "inhumane and un-Islamic."
The attackers "want to trigger a sectarian war in Afghanistan," said an Afghan Parliament member, who is one of the Shiite community's influential leaders, the Journal said. He urged the government to help maintain order.
The New York Times said the outlawed Lashkar-e-Jhangvi, which once operated openly in Pakistan with the support of its spy service, has in recent years made alliances with al-Qaida and the Pakistani Taliban.