Speaking to soldiers at an army base north of Khartoum, General al-Burhan confirmed that talks were ongoing.
"We will join hands with anyone who wants to rescue this country," he said, adding that he would not agree to anything that led to the breakup of the military.
"Everyone that was part of the organization that led to the overthrow of the regime in 2019 has the legitimate right for us to stand with them to complete this transitional period towards elections," al-Burhan said, adding that other political groups have been included as well in order to increase consensus.
Reuters reported on Friday that the military had compiled its views on a draft constitution, paving the way for steps towards a new agreement with the country's political parties.
Since the coup, members of deposed former president Omar al-Bashir's banned National Congress Party have staged a comeback in public life and the civil service. Analysts say the military has allowed this as a way to build up a new political and bureaucratic base.
On Sunday, however, al-Burhan denied that the army supported al-Bashir's National Congress Party.
"We warn those that want to hide behind the army, and specifically the National Congress Party and the Islamist Movement," he said.
"Go away, 30 years are enough, give people a chance," he added later. "Don't hold hopes that the army will bring you back."