Armed gangs are rampaging through the Central African Republic carrying out atrocities including executions and mutilations, despite the presence of French and African troops.

Reports by two leading human rights organisations say the situation in the war-torn country is out of control and requires a robust response from the international community.

Both Human Rights Watch and Amnesty International say the death toll is much higher than reported and that peacekeeping forces in the CAR must be beefed up to protect the population from further war crimes.

In its report, Amnesty says that after Christian anti-balaka (anti-machete) militia went door to door in Bangui, killing about 60 Muslims, former Séléka Coalition rebels, mainly Muslims, killed almost 1,000 people in two days of revenge attacks.

The death toll was higher than earlier UN estimates, which showed 450 people had been killed in the capital, plus 150 elsewhere.

Amnesty said its research "left no room for doubt that crimes against humanity have taken place, including extra-judicial executions and mutilation of bodies".

It added that civilians were being hacked to death and villages razed to the ground on a daily basis, even since the arrival of French and African Union forces.

The reports came as Samantha Power, the US ambassador to the UN, visited Bangui on Thursday for talks with Michel Djotodia, president of the CAR. The former rebel chief became the majority Christian country's first Muslim leader after seizing power in March.

Power said urgent action was needed to end the "vicious violence" and told victims: "We have come here to hear how you, the people of Central African Republic, are doing and how we can help."

Human Rights Watch said in its 34-page report, titled They Came To Kill: Escalating Atrocities in the Central African Republic, that during recent violence at Bossangoa, a town in the north of the CAR, parents were forced to watch as militia members slit the throats of their children. The organisation says the violence has created a humanitarian crisis.

After weeks of field research the group said the Christian militias were behind most of the violence in the region that had occurred since September this year.

It said the group had killed several hundred Muslims, burned their homes and stolen their cattle.

Reprisals by former members of the predominantly Muslim rebel alliance, which had overthrown the Bozizé government, retaliated against Christians, with the apparent knowledge of their commanders.

"The brutal killings in the CAR are creating a cycle of murder and reprisal that threatens to spin out of control," said Peter Bouckaert, emergencies director at Human Rights Watch, and the author of the report. "The UN security council needs to act quickly to bring this evolving catastrophe to a halt."

Bouckaert added: "Right now there are 1,600 French troops and 2,000 African troops in a country that is bigger than France, while there is violence in many different locations and different communities attacking each other. There just aren't sufficient troops to control the situation.

"A peacekeeping force would also include a human rights component to monitor the situation.

"But it's not just boots on the ground we are talking about. The country is effectively without government so we have to find a political solution."

Bouckaert said there was a reign of terror and while it was possible to have some control over Séléka militia groups and even some of their "extremely abusive warlords", it was more difficult to establish a relationship with, or control over, the anti-balaka, who were "more fluid … and where entire communities are armed and willing to kill".

He said: "When you have communities taking up arms against each other and massacres committed in retaliation, you are dealing with a very explosive situation. And the French and African forces are not everywhere. There are many places where there is no international presence. And even where there is … even in Bangui, the anti-balaka are using a school to recruit and train new fighters, even under the noses of the French."

Human Rights Watch said many of the attacks by the anti-balaka were shockingly brutal. One Muslim cattle herder told the organisation she was forced to watch as Christian fighters cut the throat of her three-year-old son, two boys aged 10 and 14, and an adult relative.

Another man described how a group of anti-balaka attackers cut the throats of his two wives, his 10 children and a grandchild.

On the side of the mainly Muslim former Séléka militia, killings appear to have had the backing of commanders, including that of Colonel Saleh Zabadi, who ordered the drowning of seven farmers wrongly accused of being the enemy.

About 1,600 French soldiers have been dispatched to the former French colony, working with about 6,000 African Union forces. They are attempting to disarm armed groups in the capital, Bangui, and in Bossangoa, to bring an end to the killings, create security for the local populations and enable humanitarian organisations to work.

"Urgent support for peacekeeping in the CAR is crucial to bring stability to a tense situation, protect the population from abuses, and ensure that humanitarian aid reaches those at grave risk," Bouckaert said. "The potential for further mass violence is shockingly high."