Top Welfare Minister Yusuf Kalla said such a link is possible. “Because of that we're investigating it," he added.
Earlier this month masked gunmen killed 10 people in mainly Christian villages in the Poso district of the eastern island chain.
Eight of them died in raids on three villages on 12 October, the first anniversary of the Bali bombings, which were blamed on al-Qaida-linked JI.
The killings raised fears of a return to Muslim-Christian conflict that claimed about 1000 lives in the Poso district in 2000 and 2001, until Kalla brokered a truce.
Police shot dead six suspects in the attacks and arrested 13. They will be charged under an anti-terror law.
Kalla said the recent violence was committed by a group of "hardliners" and the general public was not involved. However, he said intelligence reports on the unrest did not mention JI as being behind it.
"Intelligence reports said hardliners who fought (in the earlier sectarian conflict) have not entirely surrendered their weapons. The motive may be vengeance," he said.
Kalla however said intelligence reports on the unrest did not mention JI as being behind it
JI has eyed Poso as a potential training ground, according to a report by the International Crisis Group of political analysts.
Tempo magazine, in its edition published on Monday, quoted an anonymous JI member in Poso as saying the 12 October attacks had been carried out by the network to "commemorate one-year anniversary of the Bali bombing".
JI, which seeks to topple elected governments and create an Islamic state in Southeast Asia, was blamed for the Bali blasts, which killed 202 people and a string of other bloody attacks.
These include bomb attacks on churches and priests on Christmas Eve 2000, which killed 19 people across Indonesia.
One of the suspects arrested after the village raids is originally from Lamongan in East Java, the home of Bali bomber Amrozi.