Burhan seized power in a 2021 coup that had derailed a short-lived democratic transition following the 2019 ouster of Islamist general Omar al-Bashir.
"During our history, the armed forces have supported dictatorial governments, and we want to put an end to that," Burhan, a career soldier during Bashir's three-decade rule, said in a speech to soldiers.
Reform of the security forces in a key point of tension in discussions on a two-phase political process launched in December, envisaging generals' exit from politics once a civilian government is installed.
Critics have decried the deal, agreed by Burhan with multiple factions including a key civilian bloc, as "vague".
The proposed reforms include the integration into the regular army of the powerful paramilitary Rapid Support Forces (RSF), led by Burhan's deputy Mohamed Hamdan Daglo.
Created in 2013, RSF emerged from the Janjaweed militia that Bashir unleashed a decade earlier in the western region of Darfur against non-Arab rebels, where it was accused of war crimes by rights groups.
While experts have pointed to worrying rivalries between Burhan and Daglo, the two men took turns speaking on Sunday in the capital Khartoum, pleading for a successful integration.
Daglo said he wanted "a unified army", while Burhan called for "a professional army that stays away from politics".
The December deal came after near-weekly protests since Burhan's October 2021 takeover, which had also triggered international aid cuts, adding to the deepening political and economic troubles in one of the world's poorest countries.
Daglo, the RSF commander also known as Hemeti, said earlier this month he was against "anyone who wants to become a dictator", and that he opposed those "clinging on to power".
He said the latest coup had "failed" because it had not brought change but rather the return of the "old regime" of Bashir loyalists.