"This was an unconscionable attack on innocent pilgrims exercising their most fundamental and basic rights to freedom of religion," said Hindu American Foundation (HAF) board member Rajiv Pandit.
"We urge the Trump Administration to designate Hizbul Mujahideen as a Foreign Terrorist Organisation and clampdown on Pakistan for its continued support of Hizbul and other terrorist groups carrying out attacks in India," said Pandit.
HAF senior director Samir Kalra said Hindu pilgrims are at an "extreme risk of violence" in Kashmir.
Meanwhile, Indian-American Congressman from Illinois, Raja Krishnamoorthi also condemned the terror attack.
"My thoughts and prayers are with the victims in Amarnath and their families. Terrorism has no place in our world," Krishnamoorthi said.
Terrorists killed seven Amarnath pilgrims, including six women, and injured 19 others as they struck at a bus in Kashmir's Anantnag district last night, in the worst attack on the annual pilgrimage since the year 2001.