"Massive combing operations have started and additional troops are being rushed to the affected areas."
The wave of violence started late on Friday with 48 labourers and traders being shot dead. An explosion on Saturday killed seven people, including four policemen.
On Sunday, suspected rebels shot dead two supporters of the state's ruling Congress party after calling them out of their homes.
Security officials said the attackers had fled to the mountains of neighbouring Arunachal Pradesh state where they are said to have training camps.
Troops were in pursuit, a military commander said on condition of anonymity.
Security was tightened in areas adjoining the eastern districts of Tinsukia, Dibrugarh, Golaghat and Sivasagar to prevent the violence spilling over.
On Sunday, hundreds of people carrying bodies of some of the victims blocked roads in Doomdooma town, about 500km east of Guwahati - Assam's main city - demanding action against the ULFA.
"We want the army to kill each and every militant in this area. The ULFA should be finished once and for all," Sudhir Sharma, a trader in Doomdooma, told Reuters by telephone.
Last week the ULFA had warned non-Assamese businessmen and labourers of dire consequences if they continued to live in Assam, accusing New Delhi of flooding the state with outsiders to reduce the indigenous Assamese population to a minority.
"The ULFA's only motive behind the killings was to create panic," Gogoi said.
"Orders have been given to military and police to intensify their battle against the ULFA. There is no question of going soft on the militants."
Police said the violence was an attempt to intimidate people after an independent opinion poll by a peace group in nine districts of the oil- and tea-producing state indicated that 90 per cent of respondents rejected the ULFA's separatist demands.
Harekrishna Deka, a security analyst, said: "The ULFA wants to make it clear that government should not try to ignore it and also wants to prove that it still has the strength to strike at will."
The attacks came after officials had appealed to the rebels not to disrupt national games next month, as they have threatened to do.