The unusual incident happened along the border between Assam and Mizoram states in north-eastern India.
Officials from both sides, including chief ministers, have accused each other of provoking violence.
The firing incident follows months of simmering tensions over a long-running border dispute between the two states.
Assam shares a 164km-long (about 101 miles) border with Mizoram, and both states contest its demarcation.
The two sides have often sparred over it, sometimes violently. But this was the first time police in the states had fired at each other in a direct confrontation. The officers killed in the attack were from Assam.
The federal government has been trying to mediate a truce between the states since 1994 but has failed to achieve a breakthrough.
On Monday, Home Minister Amit Shah reportedly spoke to the chief ministers of Assam and Mizoram – Himanta Biswa Sarma and Zoramthanga – and urged them to ensure peace along the disputed border by finding an “amicable solution” to the problem.
So, what is the problem?
Mizoram and Assam, along with five other states, are in the north-east region of India, which runs from the snow-clad Himalayas just below Tibet to the plains of Bangladesh, and borders the jungles of Myanmar (Burma) to the east.
Under colonial rule, Lushai Hills, as Mizoram was then known, was part of Assam. The region only gained recognition in 1972 – almost three decades after India’s independence – when it became a separate federally administered area. In 1987, it became a fully-fledged state.
Three districts in Assam – Cachar, Hailakandi and Karimganj – share a 164km-long border with three districts of Mizoram.
The forested area is contested at several points, with both Assam and Mizoram accusing each other of encroaching on their land.
The first row broke out in 1994, leading to several rounds of talks that were brokered by the federal government. But sporadic clashes have continued.
Tensions escalated to an unprecedented level in October 2020 when residents of Assam and Mizoram clashed twice in a week. At least eight people were injured as angry residents torched huts and small shops on both sides.
At the heart of the matter was an “eviction drive” carried out by Assam along a contested part of the border – authorities from the state reportedly burned a farmhouse and crops in the area. The Mizoram government responded by deploying troops in areas which Assam claims is part of its territory.
Residents from both states also blocked key highways, bringing all traffic to a halt for almost three weeks until the federal government intervened to defuse tensions.
What happened on Monday?
Tensions escalated after clashes erupted between police on either side of a contentious border point, Lailapur, according to local reports.
Assam’s chief minister, Mr Sarma, announced on Twitter that members of the state police were killed by Mizoram forces “while defending the constitutional boundary”.
Police in Assam also alleged that “miscreants” from Mizoram pelted them with stones and attacked its government officials.
The state’s home minister, Lalchamliana, said Mizoram policemen responded “spontaneously by firing back” at Assam police officials after they “forcibly crossed” a post manned by the Central Reserve Police Force (CRPF).
The federal government has deployed the CRPF as a “neutral force” at the disputed border.
Meanwhile, chief ministers Zoramthanga and Mr Sarma argued on Twitter, blaming each other for the violence and seeking the federal government’s intervention.
Both chief ministers had attended a meeting chaired by Mr Shah in the city of Shillong on Saturday.