The Indian state of Assam has advised its residents to avoid travelling to neighbouring Mizoram after six policemen were shot dead in a rare border clash between the two regions.

India's northeast has been a hotbed of ethnic tensions since independence in 1947 and borders between its seven states are not clearly defined.

Assam and Mizoram have been wrangling over their frontier for decades, but tensions erupted on Monday with six police shot dead and more than 60 injured.

"Given the critical situation, the people of Assam are advised not to travel to Mizoram," the travel advisory issued Thursday said.

It recommended those already there "exercise utmost caution" and said "many civilians are heavily armed with automatic weapons".

India has longstanding border disputes with China and Pakistan but the clash between two of its own states has been an embarrassment for the central government led by Prime Minister Narendra Modi.

Both states have blamed each other for the violence.

K. Vanlalvena, a Mizoram politician in India's upper house, stoked tensions on Wednesday when he was quoted by media as saying his state was ready for more violence.

"More than 200 policemen entered our territory and they pushed back our policemen from our own posts and they gave firing orders first, before we fired," Vanlalvena reportedly said.

"They are lucky that we didn't kill them all. If they come again, we shall kill them all."