"I can confirm, 100 percent, that Bashir is not going to run for president in the next election. He will actually give a chance to different personalities to compete for the position," Rabie Abdul Ati, an official of his National Congress Party said on Monday to AFP.
"But he is not under pressure... This is not in the context of the change that is happening in the Arab world. It is happening because of the political strategy of the NCP broaden participation," he added, referring to a meeting of the ruling party's youth wing last week.
Abdul Ati's comments come amid fresh political turmoil in the Arab world, which has already unseated the presidents of Tunisia and neighbouring Egypt, and is now sweeping through Libya, which also shares a border with Sudan.
Bashir, who came to power in an Islamist-backed military coup in 1989, won a new five-year term of office in elections last April, despite being indicted by the International Criminal Court for war crimes and crimes against humanity in Darfur. He has since been charged with genocide.
They were the first multi-party polls since the 1986 election of the government that Bashir overthrew, but were marred by accusations of fraud and an opposition boycott.
A senior Sudanese opposition leader said the NCP comments about Bashir standing down at the next presidential election were directly related to the wave of popular unrest in the region.
"I think this is very much to do with the tsunami of people power against dictatorship in the area," Mubarak al-Fadl, a leader of the opposition Umma party, told AFP.
"Bashir feels the ground is very fragile under his feet and it is very clear that the Islamists are frustrated... They know the regime is shaky and the economic situation is very bad."
Widespread economic and political discontent have provoked sporadic protests in north Sudan since January, but the powerful security forces have maintained tight control in the capital.
Localised but vocal protests calling for regime change, civil liberties and an end to soaring price rises erupted in Khartoum and other northern cities at the end of last month, organised by students via the Internet and inspired by the protests in Tunisia and Egypt.
Police used tear gas and batons to disperse the protesters and made more than 100 arrests.
Senior Sudanese officials have said they do not fear Egypt- and Tunisia-style uprisings, and described the demonstrations in Sudan as illegal and isolated.
In addition to Sudan's economic woes, compounded by heavy debt and exhausted foreign currency reserves, the government faces criticism for the result of last month's independence referendum for the south, which returned a landslide for separation, and for its handling of the armed rebellion in Darfur.