As his warplanes rain strikes on the capital and his troops battle the paramilitary Rapid Support Forces of rival general Mohamed Hamdan Dagalo, known as Hemedti, Burhan has shown no inclination to compromise.
A career soldier in his 60s who served Bashir loyally for decades, Burhan rose through the ranks in wars in South Sudan and Sudan's Darfur region.
Hemedti, whose powerful RSF had operated alongside the army during the war in Darfur, stepped in as Burhan's deputy on the council.
They accuse him and other military leaders of killing protesters and say his coup was aimed at prolonging army rule, charges he denies.
In a grim precursor to their new conflict against each other, the army and RSF are accused of grotesque war crimes including massacres and rapes during the Darfur war.