Entitled "January 30, a word to the Sudanese youth," the Facebook site shows an angry protestor holding an Arabic placard that reads: "A better Sudan."
The call comes after Egypt's April 6 Facebook group set up by young Egyptian activists three years ago helped bring tens of thousands onto the streets this week for anti-regime rallies that have rocked the country.
With more than 10,000 followers so far, the Sudanese site calls for peaceful demonstrations in Khartoum and other Sudanese cities at 11:00 am (0800 GMT) to demand an end to "injustice and humiliation."
"We will come out to protest the high cost of living, corruption, nepotism, unemployment and all the practices of the regime, including striking women... that are contrary to the most basic laws of Islam and humanity, and violate the rights of minorities," the Facebook site says.
"We will go out to prove to the whole world that the people... will not remain silent in the face of persistent injustice and humiliation," it adds.
A source at the Popular Congress Party of Islamist opposition leader Hassan al-Turabi refused to comment on the planned protest. Other opposition parties could not be reached to say whether they would participate.
Just last week, Turabi was arrested shortly after saying that a Tunisia-style revolt, which ousted veteran strongman Zine El Abidine Ben Ali earlier this month, was likely in north Sudan.
Nationwide protests in neighbouring Egypt forced embattled President Hosni Mubarak to announce in a televised address to the nation early on Saturday that he had sacked the government and would pursue economic and political reforms.
Widespread economic and political discontent has provoked street protests in north Sudan in recent weeks, although they have been sporadic, with the army keeping tight control in the capital.
The preliminary results for Sudan's January 9-15 referendum on independence for the south, to be announced on Sunday in the southern capital Juba, are expected to deliver a landslide for secesson, which would split Africa's largest country in two in July.
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