The men were killed in raids on Friday night and Saturday morning on the remote island of Sumbawa, police spokesman Lt. Col. Agus Rianto and state news agency Antara reported. They followed the killings of two suspected militants earlier Friday on Sulawesi island, also in the east of the country.
Antara reported that the Sumbawa operations were targeting militants who had fled the Makassar. Police said those victims were behind the recent killings of two police officers in Poso district, a long established hub for Islamist militants and the scene of a vicious war between Muslims and Christians in 2001 and 2002.
Rianto said the men "were endangering the lives of officers" when they were shot but gave no more details.
Indonesia, a mostly Muslim country in Southeast Asia, has struggled against Islamist militants since its independence.
In the 1990s and early 2000s, some came under the influence of al-Qaida after waging jihad in Afghanistan and carried out four major bombings against foreign targets between 2002 and 2009. A sustained police crackdown, assisted by Western countries, has reduced the threat significantly.
However, small groups of local terrorists have carried out several attacks on police
Suspected militants have killed at least 10 police officers in incidents around the country this year.
Poso remains a vital staging ground for militants, with police saying they broke up a camp in December there. Its proximity to the southern Philippines, which is also home to Islamist extremists with known links to Indonesian ones, makes it especially significant.