A spokesman for the United Liberation Front of Asom (ULFA) said the blasts on Thursday were in response to a lack of positive response from the Indian government to its offer of peace talks.
The blasts came soon after Prime Minister Manmohan Singh rejected the group's demand for independence for the oil and tea-rich Assam state, saying it was an integral part of India. Singh said he was open to discussion of other issues.
The rebels blew up an injection well belonging to India's state-owned Oil India Ltd in the Lankachi area in the east of the state. In another incident they injured at least five soldiers in a grenade attack on an army vehicle.
They also threw a grenade at a police station but there were no reported casualties.
An Oil India spokesman said crude supply was not affected.
The blasts preceded ULFA's annual protest day on Sunday that marks the 10th anniversary of a huge army crackdown against its forces.
Prime Minister Manmohan Singh
asked rebels to shun violence
"We've put extra troops around vital installations, especially in areas through which oil pipelines pass," said state inspector general of police Khagen Sharma.
ULFA rebels often attack oil installations in Assam, which is the source of 15% of India's onshore crude oil production or about five million tonnes annually, as well as striking government and military targets.
ULFA, which took up arms for an independent homeland in 1979, has demanded independence be the core issue in any peace talks.
Singh ruled out independence during his trip to Assam that ended on Monday but said New Delhi's door was always open for negotiation with any group shunning violence.
"We've put extra troops around vital installations, especially in areas through which oil pipelines pass"
Inspector-General of Police, Assam
In October, Assam was shaken by a spate of attacks that killed 53 people and injured 150. Both ULFA and the National Democratic Front of Bodoland, which wants a separate Bodo tribal homeland, claimed responsibility.
Armed outfits in the region accuse New Delhi of plundering its resources while neglecting its development.
India's northeast is a cauldron of rebel outfits with causes ranging from autonomy to independence. More than 50,000 people have lost their lives to insurgency in the northeast since India's independence from Britain in 1947.