Bakri Hassan Saleh, a former interior and Defence Minister, was named first Vice-President as Hassabo Mohammed Abdel Rahman became second Vice-President, senior party official Rabbie Abdelatti Ebaid said.
"Yes, confirmed," Ebaid said of the appointments at the start of a government reshuffle.
Saleh was presidential affairs minister in the cabinet which Bashir dismissed last week after the most serious split in years within his ruling National Congress Party (NCP). Abdel Rahman had been the NCP's political secretary.
Saleh was a leader of the 1989 Islamist-backed coup which brought Bashir to power, Robert O. Collins wrote in "A History of Modern Sudan".
He called Saleh "an efficient and sinister defender of the revolution" who was entrusted with rebuilding the country's intelligence apparatus.
Ebaid said that final composition of the new cabinet would be declared within 24 hours, including ministers from other political parties.
Bashir had announced on Saturday that his long-time first vice president Ali Osman Taha, a key figure behind the coup, had resigned to pave the way for a new government.

"Ali Osman will voluntarily step down", as he did in 2005 following the signing of a peace agreement that ended 22 years of civil war, Bashir was quoted by the official SUNA news
agency as saying on Friday.
Taha "is the spearhead and the leader of change in the formation of a new cabinet," Bashir said without elaborating. The president hinted in mid-November that a wide-ranging government shakeup was imminent.

Last week he dismissed his cabinet ministers pending appointment of a new administration at a date which has not been announced.
Critics of Bashir's regime have become increasingly vocal since the government slashed fuel subsidies in September, leading to the worst urban unrest of his rule.
Security forces are believed to have killed more than 200 demonstrators, Amnesty International said, but the government has given a toll of less than half that.

Analysts said that the spontaneous protests pointed to an urgent need for change by the Arab-dominated regime grappling with ethnic rebellions in Darfur, South Kordofan and Blue Nile states, dissension within its own ranks, economic crisis and international isolation.
Bashir has since talked of "reform", and repeated a call for a dialogue with all political parties, including armed rebels. Taha was considered the "first" of two vice-presidents in Bashir's administration.


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