Nearly 400 people have died in northwest Myanmar, making it one of the deadliest bouts of violence to engulf the country's Rohingya Muslim minority in decades.

About 38,000 Rohingya have crossed into Bangladesh from Myanmar, UN sources said on Friday, a week after Rohingya insurgents attacked police posts and an army base in Rakhine state, prompting clashes and a military counteroffensive.

The army says it is conducting clearance operations against "extremist terrorists" and security forces have been told to protect civilians.

But Rohingya fleeing to Bangladesh claim a campaign of arson and killings aims to force them out.

UN Secretary-General Antonio Guterres is "deeply concerned" by reports of the use of excessive force during the army's operations in Rakhine state, spokeswoman Eri Kaneko said.

"(He) urges restraint and calm to avoid a humanitarian catastrophe," Kaneko said.

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The treatment of Myanmar's roughly 1.1 million Rohingya is the biggest challenge facing national leader Aung San Suu Kyi, accused by some Western critics of not speaking out for a minority that has long complained of persecution.

The clashes and ensuing army crackdown have killed about 370 Rohingya insurgents, 13 security forces, two government officials and 14 civilians, the Myanmar military said on Thursday.

The fighting is a dramatic escalation of a conflict that has simmered since October, when similar but much smaller Rohingya attacks on security posts prompted a brutal military response dogged by allegations of rights abuses.

Myanmar evacuated more than 11,700 "ethnic residents" from the area affected by fighting, the army said, referring to the non-Muslim population of northern Rakhine.

About 20,000 more Rohingya trying to flee are stuck in no man's land at the border, the UN sources said, as aid workers in Bangladesh struggle to alleviate the suffering of a sudden influx of thousands of hungry and traumatised people.

In the state capital Sittwe further south some 90,000 Rohingya have lived in camps since an outbreak of communal violence rocked the city in 2012, killing nearly 200 people.