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 three months ago, according to the UN.

The announcement on Monday came the same day as Yanghee Lee, the UN's human rights envoy for Myanmar, began a 12-day visit to probe violence in the country's borderlands.

"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.

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The exodus of Rohingya from northern Rakhine began after Myanmar's army launched clearance operations while searching for fighters behind deadly raids on police border posts in October.

Human rights groups say the military campaign has been marred by abuses so severe they could amount to crimes against humanity.

In Bangladesh, escapees from the persecuted Muslim minority 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.

READ MORE: Rohingya refugees from Myanmar tell of trauma

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.

The report 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 investigation 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.