Bhutanese forces attacked a string of rebel camps in the south of the small Himalayan kingdom on Monday, destroying several of them.
A Bhutanese government official in New Delhi said 16 soldiers were hurt in the fighting.
“Out of the 16 wounded, four are in a serious condition,” the official, who declined to be named, said.
India, which has long called for Bhutan to take action against anti-Indian rebels taking refuge there, said it was sealing the border to cut off the lines of retreat.
“When they come, they will definitely fire on us. Our troops are ready and deployed to seal the border,” Lieutenant-General Jitendra Singh Varma of the Indian army said.
India, which helps train Bhutan’s small army, says there are about 3000 guerrillas operating from 30 camps in Bhutan.
Most of the rebels come from two separatist groups battling government forces in India’s northeast, particularly in Assam state.
“We earnestly appeal to you (the Bhutanese army) to cease the ongoing operations against us as all these activities might get in the way of our legitimate struggle”
On Monday, the military commander of the biggest group operating out of Bhutan, the United Liberation Front of Asom (ULFA), said some of the group’s camps had been destroyed and his men had suffered casualties.
The chairman of the ULFA, which is fighting for the independence of Assam state, appealed to Bhutan on Tuesday to call off the offensive.
“We earnestly appeal to you to cease the ongoing operations against us as all these activities might get in the way of our legitimate struggle,” Arabinda Rajkhowa said in a statement.
He said the group’s camps in Bhutan were for “temporary refuge”.
India has put its forces on alert in three states along its 380-km border with Bhutan – West Bengal, Assam and Arunachal Pradesh.
Indian forces were also using helicopters to monitor the fighting and evacuate Bhutanese casualties if necessary, said Varma, who commands India’s eastern army.
Indian officials say the destruction of the rebel camps – most of them belonging to the ULFA and the National Democratic Front of Bodoland – will be a significant blow to groups that have launched attacks from Bhutan.