A police spokesperson said militants opened fire at a sub-divisional police officer (SDPO) while the officer was overseeing the construction of a helipad in Moreh, a trading town on the border with Myanmar.
Ethnic clashes erupted in the northeastern state on May 3 as members of the majority Meitei ethnic group and minority Kuki tribals fought over sharing government benefits and quotas in jobs and education.
Sporadic violence has continued since the peak of the clashes, despite tens of thousands of extra security personnel being deployed, marking a rare security failure for Prime Minister Narendra Modi's government in a state ruled by his Bharatiya Janata Party.
"Deeply saddened by the cold-blooded killing of SDPO Chingtham Anand .... The perpetrators will be brought to justice," the state's chief minister, N. Biren Singh, said in a social media post.
In a separate incident, militants ambushed a security convoy near village Sinam in Tengnoupal district injuring two policemen.
"Both the injured were shifted to a local hospital with multiple bullet injuries," a senior police official told Reuters by telephone on condition of anonymity.
A video showing a man's body on fire in India's restive Manipur prompted calls for justice from a minority tribal group in the northeastern state, which remains on edge more than five months after bloody ethnic clashes killed at least 180 people.
State authorities said they had ordered an investigation by the federal police into the incident suspected to have taken place on May 4.
The violence erupted on May 3 as members of the majority Meitei ethnic group and minority Kuki tribals clashed over sharing government benefits and quotas in jobs and education.
Sporadic violence has continued after the peak of the clashes despite tens of thousands of extra security personnel being deployed, marking a rare security failure for Prime Minister Narendra Modi's government in a state ruled by his Bharatiya Janata Party.
The seven second video, which surfaced on social media on Sunday and has been verified by state police, showed a man with injuries to the head lying near barbed wire while a portion of the body was ablaze.
Voices and gunshots could be heard in the background. It is unclear whether he was alive or already dead.
Authorities identified the victim as Laldinthanga Khongsai, 37, and an umbrella body of Manipur's tribal groups said he belonged to the Kuki community.
Kuldiep Singh, the state's security advisor, said the man was killed on May 4, when armed members of the two communities fought pitched battles and a mob stripped and sexually assaulted two tribal women.
"The body is still unclaimed," Singh told reporters on Monday, adding that the case will be investigated by the Central Bureau of Investigation.
The Indigenous Tribal Leaders' Forum, an umbrella body, said, "The video is a harrowing testament to the ethnic cleansing campaign against the Kuki-Zo community by the majority Meiteis."
Asserting that such "brutal acts" cannot be overlooked, the ITLF said: "The selective application of justice further reinforces our demand for a separate administration."
The Meitei make up 53% of Manipur's population, while the Kuki account for 16%.
Both sides have suffered casualties, but government data reviewed by Reuters in July showed 113 Kukis and 62 Meiteis had been killed.