"We will not tolerate injustice", she said at a rally at the Kutupalong refugee camp, near the border town of Ukhiya in Cox's Bazar district.
Chancellor Angela Merkel's spokesman, Steffen Seibert, voiced great concern about the recent violence and human rights violations during at a press conference in Berlin on Monday.
Conflicts lasting for years in Rakhine broke out again in late August after insurgents attacked many police posts and a military outpost, forcing the Myanmar army to launch operations against the insurgents.
The crisis has drawn sharp criticism from around the world.
American politicians have been growing increasingly impatient with Myanmar.
The UN Security Council will hold an urgent meeting on Myanmar's Rohingya crisis, following warnings by the organisation's human rights chief that "ethnic cleansing" is taking place. United Nations rights investigators have been barred from entering the country. "Rather, they (Islamic governments) have to increase their political, economic, and trade pressure on Myanmar's government and cry out against these crimes in worldwide organizations".
"We have received multiple reports and satellite imagery of security forces and local militia burning Rohingya villages, and consistent accounts of extrajudicial killings, including shooting fleeing civilians", Zeid said.
The Bangladesh prime minister said her country would offer Rohingyas shelter until Myanmar took them back.
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Amarpreet said they will be stocking up materials needed to prepare the community kitchen food in Dhaka.
According to Bangladesh, around 3,000 Rohingya have been killed in the crackdown.
Smoke is seen on Myanmar's side of border as an exhausted Rohingya refugee woman is carried to the shore after crossing the Bangladesh-Myanmar border by boat through the Bay of Bengal, in Shah Porir Dwip, Bangladesh September 11, 2017. The government was also fingerprinting and registering new arrivals.
Hasina, who inquired into the conditions of those arrived recently in the camp, said Bangladesh faced a similar situation during its war of liberation. Some say they were attacked by Buddhist mobs.
In the past two weeks, the government hospital in Cox's Bazar has been overwhelmed by Rohingya patients, with 80 being admitted with gunshot wounds and bad infections. They are believed to have drowned while trying to reach Bangladesh by boat.
It, therefore, called on the United Nations to invoke the principle of the "Responsibility to Protect" and intervene in Myanmar to stop the ongoing ethnic cleansing and create the conditions for the safe return and rehabilitation of the fleeing Rohingya people to their motherland.
Noting that Bangladesh had long protested the persecution of Rohingya Muslims, she told lawmakers she had "no words to condemn Myanmar".
If International organisations call on India not to deport the Rohingya Muslims, then India could cite that it is not a signatory to the 1951 Refugee Convention of the UN.