A low-level insurgency against Indonesian control has simmered for decades in Papua, the country's easternmost territory, and Jakarta has responded to the recent deadly riots by flooding the region with thousands of extra security personnel.
It also blocked internet access to quell the unrest, and on Wednesday charged a high-profile rights lawyer over spreading online videos about the riots.
"We will chase them," said national police chief Tito Karnavian.
"We already know who they are."
Karnavian pointed to exiled Papuan leader Benny Wenda and his independence movement for fomenting dissent.
"It's an old story. That is what they (Indonesia) always accuse me of," Wenda, who has lived in the United Kingdom for years, told AFP by telephone.
"It is just politically motivated," he added.
Indonesia has said the internet block was intended to stop what it described as a flood of hoaxes and provocative comments about Papuans that were stoking unrest.
Late Wednesday, the government said it had started lifting the blockade -- criticised by media and free speech advocates -- in about 29 of 42 districts across the mountainous, jungle-covered region.
"The security situation in some areas is recovering and the spread of fake news and provocative, hateful commentary related to Papua is also declining," the communications ministry said.
"The government will keep monitoring developments in areas where data services are still blocked."
On Wednesday, UN High Commissioner for Human Rights Michelle Bachelet said she was "disturbed" by the violence in Papua.
"I encourage the authorities to engage in dialogue with the people of Papua... on their aspirations and concerns, as well as to restore internet services and refrain from any excessive use of force," she said in a statement.
- Firestorm of protests -
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Indonesia took control of the former Dutch colony in the 1960s after an independence vote widely seen as being rigged.
Jakarta has refused to discuss fresh calls for an independence vote.
Most Papuans are Christian and ethnic Melanesian with few cultural ties to the rest of Muslim-majority Indonesia.
On Wednesday, authorities charged Veronica Koman, a lawyer and Papuan rights activist, for alleged incitement over a video she shared of the mid-August arrest and tear gassing of dozens of Papuan students, who were also racially abused.
A firestorm of protests broke across Papua and other parts of the Southeast Asian archipelago after the arrests in Indonesia's second-biggest city Surabaya.
Koman could face six years in jail if convicted.
"These charges are clearly intended to deter others from speaking out against human rights violations related to Papua," Amnesty International said.
Dozens have been arrested for taking part in protests and the government banned demonstrations that could lead to what it called "anarchist acts".
Indonesia has also said it is restricting foreigners' travel to Papua after four Australians were deported this week for taking part in demonstrations.
There have been conflicting reports about casualties.
Officially, five civilians and a soldier have been killed, while 15 local people and two police have been injured since the unrest broke out.
But activists say there have been more civilian deaths, with unconfirmed reports that security forces gunned down six protesters in the remote district of Deiyai last week. The government has denied those claims.
The internet blockade has made it difficult to independently verify information.