A senior Ulfa leader, however, telephoned local newspaper offices and television stations to deny its involvement.
Mahanta said the bombers had parked two bicycles fitted with carriers packed with explosives outside the Nalbari police station, which is located in a congested part of the town. These went off, killing passers-by and wounding the others.
Mahanta said police had received intelligence reports suggesting that the Ulfa was planning to avenge last week's arrest of two of the group's leaders.
The blasts came soon after New Delhi announced the government will provide safe passage to separatist leaders willing to talk and find a lasting solution to the state's problems.
Last week, suspected Ulfa fighters triggered a powerful explosion, derailing a freight train and setting more than a dozen oil-tanker railway cars on fire in Assam.
India's northeast is beset by scores of conflicts. More than 10,000 people have died in separatist violence over the past decade.
The region is home to dozens of separatist groups who accuse the Indian government of exploiting the area's natural resources while doing little for the indigenous people.