"No one has claimed the blasts, but we suspect the ULFA seems to be behind these attacks," GP Singh, the Guwahati police chief, said.
The blasts hit Guwahati before Palaniappan Chidambaram, India's home minister, arrived in the state.
"One of the bombs went off near the route the home minister was scheduled to take," a senior security official said.
The home minister was due to visit the state for a security review.
Tarun Gogoi, the state's chief minister, said: "There were security lapses. Our police force needs to be modernised and trained to deal with such terror attacks.
"The intelligence needs to be strengthened."
The ULFA is among more than two dozen armed groups in northeastern India fighting for an independent homeland or more political autonomy.
They accuse the government of plundering the oil-rich region of mineral and forest resources, neglecting the local economy.
In October, more than 80 people were killed when a series of 11 bombs exploded across Assam.
The Indian government blamed the ULFA for the attacks but it denied involvement. A group calling itself the Islamic Security Force-Indian Mujahideen later said it carried out the bombing.
During the past two decades, more than 10,000 people have lost their lives in the unrest in Assam.