South Sudanese people sit outside a nutrition clinic at a transit center in Renk, South Sudan. (AP)

The situation on South Sudan's border was "completely overwhelming" as thousands flee war-torn Sudan each day, Doctors Without Borders (MSF) warned Monday.

The medical charity said up to 5,000 people were crossing the border every day. The United Nations recently put it even higher at 7-10,000 daily.

Sudan is suffering one of the world's worst humanitarian emergencies since conflict broke out in April 2023 between the army and the paramilitary Rapid Support Forces, with tens of thousands killed and millions displaced.

An MSF emergency coordinator in Renk town, near a transit centre holding some 17,000 people according to the UN, said they were working with the International Committee of the Red Cross to provide care.

"But the situation is completely overwhelming and it's not enough," said Emanuele Montobbio.

Facilities had been expanded to accommodate the arrival of war wounded, he said, but they were unable to treat everyone.

"Over 100 wounded patients, many with serious injuries, still await surgery," Montobbio said.

Bashir Ismail, from Mosmon in Blue Nile state, was recovering in hospital in Renk after an air raid.

"Something hit me in the chest -- it was the most painful experience of my life," he said.

"I was so disoriented that it felt like I had lost my memory."

MSF South Sudan's deputy medical coordinator Roselyn Morales said thousands who had crossed faced "critical shortages of food and shelter, clean water, shelter and healthcare".

South Sudan is ill-equipped to handle the arrival of thousands seeking shelter from war, with the young country itself battling violence, endemic poverty and natural disasters.

Alhida Hammed fled to Renk after his village was attacked and he was shot in Sudan's Blue Nile state.