The Haqqani movement was formed during the Afghan resistance against the Soviet occupation of the 1980s, under Jalauddin Haqqani, its founder.
Siraj, his son, is said to have taken over the movement in recent years.
US military said that the attack on Friday had targeted leaders of the group and foreign fighters who were suspected of involvement in bomb attacks.
Separately, Afghan police said two national intelligence agents and one police officer were killed in a bombing south of the capital Kabul.
General Zalmai Oryakhain, a regional police commander, said the attack took place while the security forces were responding to another bombing that injured three police officers.