An Airbus A400M carrying the evacuees “landed safely in Jordan” at around midnight local time (2100 GMT), the Bundeswehr said on Twitter.
A total of three A400Ms had reached Sudan on Sunday to pick up people to be evacuated, it added.
The aircraft was carrying nationals of other countries as well as German citizens, an army spokesman said.
Defence sources told AFP the German military planes were taking off from Azraq in Jordan and using a Sudanese airport near the capital Khartoum, about a three-hour flight away.
The foreign and defence ministries had earlier said they were conducting “an ongoing evacuation operation… in coordination with our partners”.
“Our aim is to fly as many (German) nationals out of Khartoum as possible in this dangerous situation in Sudan,” the ministries wrote on Twitter.
“Within the scope of our possibilities, we will also take EU and other nationals with us,” they added.
Several other nations have also begun evacuating their citizens from Sudan, including the Britain, France and United States.
Germany had aborted an attempt to begin evacuations on Wednesday, according to Der Spiegel magazine.
Three military transport planes headed for the country but were made to turn back, it said.
The Bild daily reported on Sunday that the German government was planning to rescue around 300 German citizens.
A ceasefire has been agreed for the duration of the mission, it said.
Bild also reported that paratroopers from the German army have been sent to Jordan to potentially help with further evacuation efforts.
The fighting between army chief Abdel Fattah al-Burhan’s forces and his former deputy Mohamed Hamdan Daglo’s Rapid Support Forces began on April 15 over a dispute on the planned integration of the RSF into the regular army.
The violence has left at least 420 dead and 3,700 injured, according to the World Health Organization.
AFP
