"The health situation in Sudan wasn't at its best anyway, and it is becoming more and more challenging," Sudan's Foreign Affairs Minister Omar Qamareddine said, as emergency aid from Bahrain arrived on Monday.
Over 110,000 homes have been damaged or destroyed by floodwaters, according to the government, increasing the risk of water-borne diseases and hampering efforts to stem the spread of novel coronavirus.
"People will need more and more medicines and they will need mobile medical units because it's a huge country," Qamareddine added.
At least 650,000 people have been affected since the start of the rains in mid-July, more than 110,000 in the first week of September alone, the United Nations said Monday, quoting figures from Sudan's Humanitarian Aid Commission.
Over a hundred people have been killed and more than 50 injured in the floods, according to the Sudanese civil defence.
"The unprecedented flooding has surpassed the forecast and partners are running out of supplies," the UN Office for the Coordination of Humanitarian Affairs (OCHA) said.
More flooding is predicted in coming days with heavy rains forecast upstream in neighbouring Ethiopia, OCHA added.
Qamareddine said that aid needs were "huge", but that the response from Arab countries had been "very good".
Egypt, Saudi Arabia and the United Arab Emirates have sent tonnes of aid to Sudan in recent weeks, but Qamareddine said more was needed.
"We are asking the international community to move a little faster to help," he said.
Qamareddine added that US Secretary of State Mike Pompeo "also promised to help with some emergency assistance".
Heavy rains usually fall in Sudan from June to October and the country faces severe flooding every year.
But officials have recorded the highest water levels on the Blue Nile -- which joins the White Nile in the Sudanese capital Khartoum -- since records began over a century ago.