Previous talks aimed at ending the conflict that has created the world's largest humanitarian crisis have failed with both sides failing to deliver on their promises.
More than 10 million people have fled their homes since former allies clashed over a political plan to move toward internationally backed civilian rule.
The Jabit military base is about 100 km (62 miles) from Port Sudan, the military's de facto capital and where General Burhan is stationed.
Video shared by those who attended the event Wednesday morning shows military graduates marching in their ceremonial attire before the sound of gunfire can be heard.
“The only force that is hostile to the Sudanese people and is targeting the Sudanese people is the Rapid Support Forces, which is a rebel group,” General Abdullah told the BBC.
He thanked God that General Burhan and “all the commanders present were safe” and that there were not many serious casualties.
The Beja people, who live in this area between the mountains and the Red Sea coast, have been in conflict with those in power for decades, often feeling ignored and marginalized.
These communities are often at odds with one another, but they generally support General Burhan, despite anger at the rising cost of living as many flee the capital Khartoum and arrive in Port Sudan.
Only the military and the RSF are allowed to use drones, and both sides use them extensively.
There have also been claims in recent months that various factions within the military are at odds.
Some analysts point to an incident in April when several commanders of a military brigade called Abbara Ivan Malik were killed in a drone strike in the northeastern city of Atbara during the Islamic holy month of Ramadan.
Analysts said the brigade was likely made up of hardline Islamists who oppose peace talks and may have been targeted by moderates within the military.
However, some experts claim that the RSF is increasingly using drones to target areas controlled by the military.
According to Reuters, RSF controls eight of Sudan's 18 provincial capitals, including Khartoum, and is expanding further into the country's southeast.
Sudan's Foreign Ministry requested a meeting with U.S. officials on Tuesday ahead of talks that begin in Geneva on August 14.
RSF accepted the US invitation shortly after it was proposed last week.
