Lashkar-e-Jhangvi spokesman Abu Bakar telephoned journalists in Quetta, the capital of Balochistan province, to claim responsibility for yesterday's attack.
He said the attack was carried out in retaliation for the recent bombing of a madrassa and a Tablighi Jamaat centre in Quetta.
Balochistan Home Secretary Naseebullah Bazai confirmed to the media that the attack was carried out by a suicide bomber.
The attacker rammed his explosives-laden vehicle into the bus that was carrying Shia pilgrims returning from Iran.
Two policemen escorting the pilgrims were among the dead.
Police said they had arrested about two dozen suspects during raids in different parts of Quetta.
Balochistan has become a flashpoint for sectarian and ethnic violence.
In several recent attacks, suspected LeJ militants have stopped buses, separated members of the minority Hazara Shia community from other passengers and gunned them down in cold blood.
Shia groups observed a strike today to mourn those who died in yesterday