Five soldiers were killed instantly, Aind said. The wounded soldiers, at least 33 in critical condition, were taken to nearby hospitals.
The first bus was reduced to a mangled heap of metal by the powerful blast, said Aind, speaking by telephone from Goalpara. Some soldiers in the second bus were also wounded.
Initial investigations indicated the rebels belonged to the National Democratic Front of Bodoland, an insurgent group that has fought for independence from India since 1986, Aind said.
Hours after the explosion a man who said he belonged to another separatist group, the United Liberation Front of Asom, or ULFA, called local television channels and claimed responsibility for the blast.
"After our recent reverses we were dismissed as a weak force. But here we are to prove our strength," the caller said, identifying himself as Anu Buragohain. ULFA would carry out more strikes if security operations against the group were not stopped, he said.
It was still unclear which group was responsible. Officials said there was no known activity by ULFA in the area, whereas Goalpara was known as a National Democratic Front of Bodoland stronghold.
"We are investigating from all angles to pinpoint the rebel group responsible for the attack," Aind said.
The NDFB and ULFA are among the main separatist groups in Assam. More than 30 northeastern separatist groups have fought for decades for independence from India or greater autonomy in Assam, about 1,000 miles (1,600 kilometers) east of the capital, New Delhi.
The militants say the Indian government exploits the region's rich natural resources while neglecting the development of the region.
The NDFB leader, Ranjan Daimary, was handed over to Indian authorities by the Bangladesh government in May. He is in jail awaiting trial in Goalpara.
NDFB rebels have stepped up attacks since Daimary's arrest. On Monday, they ambushed a jeep killing four paramilitary soldiers and wounding another three in Assam's Chirang district.