UN High Commissioner for Refugees Filippo Grandi, who is on a visit to Ethiopia, called for "urgent and additional support to meet their needs," his agency said in a statement disclosing the numbers.
The conflict between Sudan's army chief Abdel Fattah al-Burhan and his former deputy, Mohamed Hamdan Daglo, commander of the paramilitary Rapid Support Forces (RSF), erupted in mid-April last year.
Diplomatic efforts to end the violence continue but have failed to bear fruit, and numerous ceasefires have been broken.
Nearly eight million people have been displaced internally or fled to other countries by the "brutal conflict," the UN said.
"I heard stories of heartbreaking loss of family, friends, homes and livelihoods," Grandi said in the statement.
Over 100,000 people have fled into Ethiopia, one of the six neighbouring countries sheltering the refugees, according to UN estimates.
The number of people who have gone to Chad since the war began crossed 500,000 last week, and an average of 1,500 flee into South Sudan each day, the UN statement said.
"Without further donor support, it will be extremely difficult to deliver much-needed help to those who need it most," Grandi said.
The Sudan war has killed at least 13,000 people, according to a conservative estimate by the Conflict Location and Event Data project.
Both sides have been accused of war crimes, including the indiscriminate shelling of residential areas, torture and arbitrary detention of civilians.
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