Myanmar leader Aung San Suu Kyi is coming under more pressure by the international community to end the violence against the minority Rohingya Muslims.
In the last two weeks alone some 290,000 mostly Rohingya civilians have fled to Bangladesh, overwhelming refugee camps that were already bursting at the seams, the UN has said.
Others have died trying to flee the fighting in Rakhine state, where witnesses say entire villages have been burned.
On the basis of witness testimonies and the pattern of previous outbreaks of violence, said Yanghee Lee, the UN special rapporteur on human rights in Myanmar, "perhaps about a thousand or more are already dead".
"This might be from both sides but it would be heavily concentrated on the Rohingya population."
Many countries with large Muslim populations, including Pakistan and Turkey, have expressed concern over the
violence and called on Suu Kyi to act.
An online petition signed by more than 386,000 people on Change.org is calling for Suu Kyi to be stripped of her Peace Prize over the persecution of the Rohingya.
She received the award for "her non-violent struggle for democracy and human rights" while standing up against military rulers.
Bangladesh has struggled to cope with those fleeing the violence, which takes the number of Rohingya refugees in camps on its border with Myanmar to around 690,000.
Of these, nearly 357,000 -- a third of Myanmar's total Rohingya population -- have left since October when the latest upsurge in violence began.
While the world has focused on Bangladesh, a serious humanitarian crisis is also unfolding on the Myanmar side, aid workers say.
The Red Cross organizations are scaling up operations in Myanmar's violence-riven northwest, after the UN had to suspend activities there following government suggestions that its agency had supported Rohingya insurgents.
"The UN and INGOs have not been very welcome in Rakhine and...they are not able to operate and ensure the safety and security of their staff and volunteers," said Joy Singhal of the International Federation of Red Cross and Red Crescent Societies (IFRC).
"In such an environment, the government has invited the Red Cross to assist them," Singhal said.