Kutupalong Refugee Camp, Bangladesh (CNN) They have come in their thousands, crossing hills and rivers, marshes and rice paddies for the chance to cross into Bangladesh and escape the mass killings they say are being perpetrated against their people.

The UN estimates that, in just over one week, more than 70,000 Rohingya -- a stateless, ethnic Muslim minority who largely inhabit Myanmar's western Rakhine state -- have fled escalating violence.

Refugees tell CNN the Myanmar army attacked them. The government blames "terrorists" for initiating the violence.

An estimated 73,000 refugees have crossed into Bangladesh since last Friday, UNHCR spokeswoman Vivian Tan told CNN.

On Thursday, the bodies of 20 Rohingya were pulled out of the Naf River along the border of Myanmar and Bangladesh. Twelve of the dead were children.

People gather around covered dead bodies of Rohingya children who died after a boat carrying Rohingya people capsized.

Beaten, shot at, hacked to death

The testimonies of Rohingya sheltering in overcrowded Bangladeshi refugee camps are harrowing.

"They are beating us, shooting at us and hacking our people to death," Hamida Begum, one refugee who has left everything behind in a desperate attempt to flee with at least their lives, told CNN.

"Many people were killed. Many women were raped and killed. We are very poor. My husband is a day laborer," she said.

"Begum" is an honorific given to some Muslim women, while others use it to replace their last name upon marriage.

"We used to have two square meals a day. But we lost everything after the war started," she said, referring to the outbreak of violence last Friday when Rohingya militants staged co-ordinated attacks on border posts, killing 12 security officers.

In response, the military intensified "clearance operations," driving thousands of people from their homes.

Government officials said Thursday that at least 399 people had been killed in fighting since last Friday. Of those, 370 were "terrorists," they said. However, activists say the military has killed women, children and innocent men.

Both sides also blame each other for torching houses. The government says Rohingya militants have burned down more than 2,300 homes . The Rohingya says it's the military that has attacking their houses.

Begum alleges that her family was tortured by the military and their accomplices, and that others were killed after failing to pay the soldiers a ransom.

"We had to flee to save our lives. They don't allow us to move freely. We were deprived of everything... They are picking up people from home and asking them for ransom. Many of (those people) were shot dead."

CNN can't independently verify the stories of those who fled, and the Myanmar government has not responded to a request for comment.

A Rohingya man, carrying what he could from his home in Rakine, walks towards the Kutupalang unregistered camp to look for shelter.

Aid organizations and the UN have slammed the Myanmar government for its treatment of the group.

"Decades of persistent and systematic human rights violations, including the very violent security responses to the attacks since October 2016, have almost certainly contributed to the nurturing of violent extremism, with everyone ultimately losing," Zeid Ra'ad Al Hussein, UN High Commissioner for Human Rights, said Thursday.

'Only the Rohingya are hated'

There are many ethnic groups in Myanmar "but only the Rohingya are hated by the government," said Mohammad Harun, who was among those fleeing.

The Rohingya are a minority Muslim population in Myanmar, however they're denied the right to citizenship despite having lived there for generations.

Another refugee interviewed by CNN said the military ordered them to stay inside their homes.

"If we stay inside then they set our houses on fire, shooting at us or slaughtering us," Nobin Shuna says. "Muslims have no rights."

A Rohingya man carrying his mother after crossing the Bangladesh-Myanmar border.

She says the military came to her village last Friday and killed five people, including her son.

"They were tortured to death. Our houses were set on fire. We lost everything there," she said.

"How could we survive? I have no money. After seeing the massacre, I traveled all the way to the Bangladesh border. I left my home four days ago. Now where would I go? My son was killed."

And so now these thousands trek westwards, towards the relative safety of neighboring Bangladesh.

An estimated 200,000 to 500,000 Rohingya refugees already live a precarious existence here, most in squalid, overcrowded camps.

'Disproportionate response'

Last year, as many as 85,000 Rohingya crossed the border following a similar spate of violence. The persecution of this people has been going on for decades, said Sally Smith, Executive Director of the Nexus Fund, an NGO committed to "preventing mass atrocities."

"In the last few days, this is very similar to what happened in October, when you had a small-scale attack by a small number of Rohingya insurgents," Smith told CNN.

"That led to a really disproportionate response by the Myanmar military against civilians, killing them, raping them, even firing machine guns at innocent men, women and children as they're running toward the border to flee into Bangladesh.

"They're burning down villages --- it's just not OK to attack civilians."

An elderly Rohingya man smokes the last of his Burmese cigar while looking for shelter in Bangladesh with his family near Kutupalang unregistered camp.

She says that Myanmar's leader, Aung San Suu Kyi, has been "disappointing" in her refusal to condemn the attacks.

"She's a Nobel peace prize winner and what it seems is happening is that she does care about peace for Buddhists, but not for the Rohingya.

"Right now she's using language which is incredibly irresponsible and inflammatory, she's saying that these are terrorists and that's only going to increase what's happening and the tensions that are rising and it's going to give rise to civilian attacks against Rohingya as well."

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Suu Kyi has denied some of the more severe allegations made by rights organizations, including that ethnic cleansing is occurring in the region. But so far she has not made a strong public statement to condemn the attacks.

Homeless, hungry, hopeless

The journey itself to Bangladesh, refugees say, is arduous.

"We had walk a long a way. We had to cross hills, marshes and paddy fields to make the journey to Bangladesh border," Rabeya Khatun said from Kutupalong unregistered camp, on the Bangladeshi side of the Naf River.

"I left my home eight days ago. I've reached here today."

Now they're safe from the military but still living a parlous existence.

"We have no food and no clothes. We are homeless," said refugee Mohammed Harun. He says he cannot go back -- the military has destroyed their food supplies, razed their homes.

"Everything, destroyed by the military. Now we are without food or blankets."

"Genocide is going on there."

Rohingya refugee Ramiza Begum fled to Bangladesh with her family, leaving everything behind in Myanmar. She tells CNN her house was burned down.

Many left their homes with just the clothes on their backs, bringing with them only stories of murder, rape and villagers torched.

"I could not bring anything," Romiza Begum says, her white hair peeking out from beneath her patterned headscarf, one of the items of clothing she had to accept as charity.

"These clothes were given (to me) by someone here. I asked for clothes. I lost everything. There is nothing left in my home in Burma. Everything is destroyed."