The head of the UN's refugee agency Filippo Grandi said on Tuesday that the number of people who have fled the fighting in Sudan was now more than 500,000 while two million are internally displaced.

"Today we pass the mark of half a million refugees from Sudan following the beginning of the conflict," he said at a press conference in Nairobi.

"Two million people are displaced inside the country."

Sudan has been riven by conflict since April 15, with the army led by Abdel Fattah al-Burhan battling the paramilitary Rapid Support Forces (RSF) commanded by his former deputy, Mohamed Hamdan Daglo.

"If we don't silence those guns, the exodus of Sudanese people will continue," said Grandi, the United Nations High Commissioner for Refugees.

He was speaking on World Refugee Day, a day after donors at a UN conference pledged close to $1.5 billion to combat the humanitarian crisis in Sudan and help its neighbours host those fleeing the fighting.

More than two months into the fighting, the United Nations voiced fears the crisis could spill over and destabilise neighbouring African states.

"The scale and speed of Sudan's descent into death and destruction is unprecedented," UN Secretary General Antonio Guterres told the donor conference on Monday.