He was speaking after the president, the leader of the coup and his successor had all resigned because of continued street protests.
The former Sudanese leadership planned to quell mass anti-government protests in Khartoum using military force, that is why the country's military ousted President Omar Bashir from power, a spokesman for Sudan's transitional military council, Shams al-Din Kabashi Ibrahim, said on Sunday.
The political parties and movements behind the four months of protests said in a joint statement late Saturday that they will remain in the streets until their demands are met. The council met Saturday with a delegation of protest organizers.
SPA, which had demanded civilians be included on the transitional military council and for Bashir's close associates to leave, called for the arrest of prominent National Intelligence and Security Service generals, including its former head Salah Gosh, and for the removal of the prosecutor general.
Meanwhile, the party of Sudan's ousted president has slammed the military's power grab as unconstitutional.
Saudi Arabia said it "stands by the Sudanese people" and called on all Sudanese "to give priority to the national interest" of their country.
The agency added that Riyadh had also announced a humanitarian aid package to Sudan, including wheat, petroleum products, and medicine.
"The ministry of foreign affairs is looking forward to the worldwide community to understand the situation and to support the transitional military council.in order to achieve the Sudanese goal of democratic transition", the ministry said in a statement.
On Saturday the UAE's Ministry of Foreign Affairs and International Co-operation welcomed Gen Al Burhan's appointment as a "step forward reflecting the ambitions of the brotherly people of Sudan towards security, stability and development".
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Protests have been about the economic conditions in the country but extended to ending the military regime led by Mr. Bashir.
After being sworn in by the head of the constitutional court, Burhan called on the opposition to meet with the military council now running the country in order to form a new government.
He also vowed to bring to justice individuals involved in the killing of protesters, as well as those from the toppled regime involved in corruption cases.
Burhan took the oath of office on Friday after his predecessor General Awad Ibn Ouf stepped down little more than 24 hours after Bashir's ouster.
The face of the coup, ibn Ouf was himself head of military intelligence during the brutal campaign to suppress the Darfur insurgency.
In remarks broadcast on state TV, Burhan said Saturday that the council has invited "all spectrums of Sudanese people for dialogue".
Al-Bashir imposed a state of emergency in February, banning unauthorised public gatherings and granting sweeping powers to the police in efforts to quash the unrest.
The protesters have modeled their movement on the Arab Spring uprisings in 2011 that swept leaders from power in Egypt, Tunisia, Libya and Yemen.
Dozens of people have been killed in protest related violence since demonstrations erupted against Bashir's rule in December. They reiterated their rejection of military rule.