The army unleashed a counter-insurgency campaign against the Arakan Army, which recruits from the region’s mostly Buddhist ethnic Rakhine population, almost a year ago.
The militants are fighting for greater autonomy from the central government, and authorities cut internet access to most of the region in June.
Tens of thousands of people have been displaced across Rakhine since clashes began in December last year, bringing fresh chaos to the region, from which more than 730,000 Rohingya Muslims fled a military crackdown in 2017.
Two military spokesmen did not answer phone calls from Reuters seeking comment, while a spokesman for the Arakan Army also blamed the army for the shelling, saying there were no clashes involving its fighters in Mrauk U.