Witson Sangma was arrested on charges of supplying explosives to the outlawed Garo National Liberation Army (GNLA). He was Wednesday found dead in police lockup.
This was the second custodial death. The first was Balsan Marak, 20, accused of illegal confinement, kidnapping and torture of 12 women, including a pregnant woman, who died at the Tura Civil Hospital May 20.
Police said Sangma's death was due to hypertension, residents alleged "police excesses".
Warjri said, "I appeal to all sections of society to maintain peace and harmony and not to believe rumour mongers."
He said the district administration had stepped up security and officials were meeting people to restore normalcy.
"Two separate magisterial inquiries and another high-level probe headed by commissioner of division (Garo hills) Peter J. Ingty has been constituted into the deaths. The government will punish if anyone is found guilty in both (custodial deaths)," Warjri said.
Additional District Magistrate T.G. Momin told IANS over phone: "The situation is tense but under control. Curfew is still on in Chokpot block of South Garo Hills to prevent the situation from escalating."
He added: "Peace meeting has been initiated between the administration, civil society groups and religious leaders."
Civil society groups, including the powerful Garo Student's Union (GSU) have announced non-cooperation movement June 2 in all the five districts of Garo Hills over the custodial deaths.
The groups are demanding a CBI or a judicial inquiry into the deaths and want an independent body carry out the autopsies.
"If the government does not heed to our demand by Friday, we will agitate," GSU leader Tengsak Momin said.
The Meghalaya People's Human Rights Council (MPHRC) criticised police over their abysmal record of custodial deaths.
"In Meghalaya, 20 people have died in police and judicial custody between 2001 and 2013. There is much evidence from various verdicts of the judiciary and the National Human Rights Commission (NHRC) that a majority of these deaths are a direct implication of torture by police in custody, which is a clear violation of human rights," MPHRC chairman Dino D.G. Dympep said.