The conflict between the army and the paramilitary Rapid Support Forces (RSF) has also led to worsening hunger, with some people eating soil or leaves as famine looms.
Faki condemned external interference and reiterated AU's demand for 'foreign countries' to cease the supply of weapons to the belligerents.
The Security Council, in a statement, "expressed their deep concern over an imminent offensive by the Rapid Support Forces and their allied militias" against the city of al-Fashir.
The war between the army and the paramilitary RSF has creasted the world's largest displacement crisis.
Today Chad is home to almost a million Sudanese refugees -- more than any other country.
During the current war, government forces have used their air power to bomb targets on the ground, but failed to gain back much territory and have been blamed for striking civilians.
The UN says it has been able to reach only 10 per cent of Sudan's 48 million people, with the country on the brink of famine.
The UN agency reported on Friday that 37 trucks carrying 1,300 tons of supplies crossed last week into West Darfur from Adre in Chad
The Zamzam camp in North Darfur is one of the largest camps for displaced people in the country.
Baerbock's multi-day trip will take her to South Sudan, Kenya and Djibouti, where she will also discuss ways to protect shipping in the Red Sea from attacks by Yemen's Huthi rebels.
Sudan's paramilitary Rapid Support Forces (RSF) announced on Tuesday their readiness to enter immediate and unconditional ceasefire discussions with the Sudanese army.
According to the United Nations, the violence has caused more than 9,000 deaths and forced over 5.6 million people to leave their homes in the past six months.