“According to our information there is heavy rain in Ethiopia, and we expect flooding in the coming days,” Abdallah Khiar told reporters.
Rains in Ethiopia feed into the Blue Nile river which runs to Khartoum, Sudan’s capital.
The city has already been worst-hit by the heavy rains and flash floods which began in Sudan on August 1 and inundated several states, according to the United Nations.
More rain is expected in Khartoum through Friday, Khiar said.
The Blue Nile has already begun to overflow its eastern bank but is about one metre below the reinforced west bank, an AFP correspondent observed in east Khartoum.
Fifty-three people around the country have died and 40 000 families, or about 200 000 people, have been affected, Interior Minister Ibrahim Mahmoud Hamed told the same press conference.
AFP found residents of a community east of the Blue Nile camped beside the road on Wednesday because their homes had been destroyed or damaged in the flash flooding.
They appealed for more aid but Hamed told reporters “the situation is under control” and there is no need to declare an emergency.
“We have stocks of medicine, food and shelter material to support the affected people,” he said.
Qatar, Ethiopia and Egypt have already flown in aid.