Indian rebels fighting against the Bhutanese army say they have told around 200 of their women, children and injured fighters to surrender.
Some 6,000 Bhutanese troops have been deployed
The United Liberation Front of Assam (Ulfa) said the Bhutanese army had agreed to accept them.
Over 120 people have died since Bhutan launched its first offensive against Indian rebel groups on Monday.
Three rebel groups have used Bhutan as a base for operations against India for the past decade.
Ulfa told the BBC's Subir Bhaumik in Calcutta that it had appealed to the Red Cross to intervene to protect the women and children.
However, group spokesman Rubi Bhuyan said there had been no response and the rebels were left no choice but to surrender the families and injured.
An Indian army official said Ulfa was trying to use the Red Cross to secure safe passage for their rebels and allow them to escape capture.
Lieutenant-General Jitender Singh Varma said if the Red Cross went into Bhutan most of the rebels would hide their weapons and register with the international organisation as sick or non-combatants.
He said most of the rebels had fled from their bases and gone into the jungles of southern and western Bhutan.
Several leaders have been captured, but General Varma said the top Ulfa leaders, Paresh Barua and Aurobindo Rajkawa, had escaped to Bangladesh.
About 6,000 Bhutanese troops have destroyed almost all of the 30 rebel camps in the country during the offensive, officials say.
The camps were said to have sheltered about 3,000 rebels.
Indian troops have been deployed on the country's border with Bhutan to prevent rebels from fleeing into India.
The three rebel groups are Ulfa, the National Democratic Front of Bodoland (NDFB) and the Kamtapur Liberation Organisation (KLO).
Ulfa is fighting for Assam's independence from India while the NDFB and the KLO are fighting for separate tribal homelands.