Earlier in the day, Sudanese army said it will make an "important statement soon", state television and radio announced, as thousands of protesters camped outside the military headquarters in Khartoum demanding the resignation of President Omar al-Bashir.
He also said a three-month state of emergency was being put in place.
But it was a government decision to triple bread prices that brought protesters onto the streets in December past year, as the country grappled with regular shortages of food, medicines and foreign currency.
The military removed Nimeiri after a popular uprising in 1985. Instead, they demand a civilian transitional government.
"We are calling on our people to control themselves and not to attack anybody or government and private properties", the Alliance for Freedom and Change (AFC), the umbrella group that is spearheading the protest movement, said in a statement.
Bashir, who is wanted by the International Criminal Court on charges of war crimes and genocide, came to power in a 1989 coup.
Protesters outside the ministry chanted: "It has fallen, we won".
The minister of production and economic resources in North Darfur Adel Mahjoub Hussein confirmed consultations are under way to set up a transitional council to run the country.
Sudan's intelligence service said it was freeing all political prisoners.
Mr Ibn Ouf said the country had been suffering from "poor management, corruption, and an absence of justice" and he apologised "for the killing and violence that took place".
Sudan's protests initially erupted last December with rallies against a worsening economy, but quickly escalated into calls for an end to embattled al-Bashir's rule.
As public anger grew, Bouteflika announced he would not stand in the polls and delayed elections without setting a new date.
As the Khartoum sit-in surged in size, the government responded with an increased crackdown.
A massive crowd of jubilant Sudanese people thronged squares and streets of central Khartoum ahead of the announcement.
Army vehicles carrying troops were seen deploying across the center of Khartoum from early Thursday. The witnesses spoke on condition of anonymity because they feared reprisals. And martial music was played on state television as soldiers ordered the TV to halt its normal programming.
Scores were killed in violent repression of the demonstrations, and the armed forces eventually refused to use their weapons against the Malian people.
In November past year, Sudan's Petroleum Minister Azhari Abdalla said that the country wanted to attract oil investments and would launch an exploration bid round in 2019, probably in the third quarter.
Sarah Abdel-Jaleel, a spokeswoman for the Sudanese Professionals Association, tells The Associated Press they will not back a military coup and insist on an "unconditional stepping down of al-Bashir and his regime".
"We are waiting for big news", one protester told AFP from the sit-in. It was his first such speech since he imposed a state of emergency across the country in February. Omar al-Bashir, with the support of military officers and an Islamist political party, took power as leader of a junta in his own coup on June 30, 1989.
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