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The conflict in Sudan has displaced more than one million children, 270,000 of them in the Darfur region, the UN children's agency (UNICEF) has said, warning more were at "grave risk".

Fighting has raged in Sudan since mid-April between army chief Abdel Fattah al-Burhan and his former deputy Mohamed Hamdan Daglo, who commands the paramilitary Rapid Support Forces (RSF).

As well as the more than one million displaced, at least 330 children have been killed and more than 1,900 wounded, UNICEF said in a statement on Thursday.

"Many more are at grave risk".

The United Nations agency said an estimated 13 million children were in "dire need" of humanitarian assistance.

"Children are trapped in an unrelenting nightmare, bearing the heaviest burden of a violent crisis they had no hand in creating -- caught in the crossfire, injured, abused, displaced and subjected to disease and malnutrition," said UNICEF Sudan representative Mandeep O'Brien.

It said the situation in Darfur, already scarred by a two-decade war that left hundreds of thousands dead and more than two million displaced, was especially concerning.

"The situation in West and Central Darfur, in particular, is characterised by active fighting, severe insecurity and looting of humanitarian supplies and facilities," UNICEF said.

Daglo's RSF have their origins in the Janjaweed militias which former strongman Omar al-Bashir unleashed on ethnic minorities in the region in 2003, drawing charges of genocide, war crimes and crimes against humanity.

Its paramilitaries have been accused of carrying out the Wednesday killing of West Darfur state governor Khamis Abdullah Abakar hours after he made remarks critical of the paramilitaries in a telephone interview with a Saudi TV channel. The RSF has denied any responsibility.

The United Nations said "compelling eyewitness accounts attribute this act to Arab militias and the RSF", while the Darfur Lawyers Association condemned the act of "barbarism, brutality and cruelty".

"All those responsible for this killing must be held to account including those who bear command responsibility," Jeremy Laurence, spokesman for the UN rights office, told reporters in Geneva.

Ìý'Ominous reminder' -

The US State Department said the atrocities unfolding in West Darfur were "primarily" the work of the RSF and provided an "ominous reminder" of the region's previous genocide.

"The United States condemns in the strongest terms the ongoing human rights violations and abuses and horrific violence in Sudan, especially reports of widespread sexual violence and killings based on ethnicity in West Darfur by the Rapid Support Forces (RSF) and allied militias," State Department spokesperson Matthew Miller said.

"The atrocities occurring today in West Darfur and other areas are an ominous reminder of the horrific events that led the United States to determine in 2004 that genocide had been committed in Darfur."

Miller said up to 1,100 civilians had been killed in the West Darfur state capital, El Geneina, alone.

"While the atrocities taking place in Darfur are primarily attributable to the RSF and affiliated militia, both sides have been responsible for abuses," he added.

Now in its third month, the fighting has claimed more than 2,000 lives, according to the Armed Conflict Location and Event Data Project.

The International Organization for Migration says the fighting has driven 2.2 million people from their homes, including 528,000 who have fled to neighbouring countries.

With mediation efforts at a standstill after repeated abortive ceasefires, the fighting has raged on unabated.

In Khartoum North, just across the Blue Nile from the capital, the regular army carried out air strikes drawing anti-aircraft fire from the RSF, witnesses said.

Across the Nile in Omdurman, an air strike hit the Beit Al-Mal neighbourhood, killing at least three people and damaging several houses, the neighbourhood "resistance committee" said.

The RSF said the strike killed 20 people, some inside a mosque, and accused the regular army, which has a virtual monopoly of the skies, of carrying out multiple strikes on residential neighbourhoods.

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