Rohingya Muslims from Myanmar, who tried to cross the Naf river into Bangladesh to escape sectarian violence, are kept under watch by Bangladeshi security officials in Teknaf on December 25, 2016 (AFP Photo/STR)

At least 65,000 Rohingya have fled to Bangladesh from Myanmar -- a third of them over the past week -- since the army launched a crackdown in the north of Rakhine state, the UN said Monday.

The figure marks a sharp escalation in the numbers fleeing a military campaign which rights groups say has been marred by abuses so severe they could amount to crimes against humanity.

They also come the same day the UN's human rights envoy for Myanmar, Yanghee Lee, began a 12-day visit to probe violence in the country's borderlands that will take her to the army-controlled area.

"Over the past week, 22,000 new arrivals were reported to have crossed the border from Rakhine state," the UN's relief agency said in its weekly report.

"As of 5 January, an estimated 65,000 people are residing in registered camps, makeshift settlements and host communities in Cox's Bazaar" in southern Bangladesh, said the Office for the Coordination of Humanitarian Affairs.

The exodus of Rohingya from northern Rakhine began after Myanmar's army launched clearance operations while searching for insurgents behind deadly raids on police border posts three months ago.

Escapees from the persecuted Muslim minority in Bangladesh have given harrowing accounts of security forces committing mass rape, murder and arson.

The stories have cast a pall over the young government of Aung San Suu Kyi, with mainly Muslim Malaysia being especially critical.

Myanmar's government has said the claims of abuse are fabricated and launched a special commission to investigate the allegations.

Last week it presented its interim report denying accusations of "genocide and religious persecution" and saying there was insufficient evidence that troops had been committing rape.

That judgement came days after a video emerged showing police beating Rohingya civilians, something the government said was an isolated incident after the officers were arrested.

On Monday the UN's Lee began her own probe with a visit to Kachin state, where thousands have been displaced by fighting between ethnic rebels and the army.

Lee, who has faced threats and demonstrations on previous visits over her comments on Myanmar's treatment of the Rohingya, is due to visit Rakhine before leaving on January 20.

Hardline Buddhist monk Wirathu caused outrage when he called her a "whore in our country" for criticising controversial legislation considered discriminatory to women and minorities.