Organisers are calling for tens of thousands of people to gather in Tahrir Square, where days of unrest have left at least 300 people dead.
Mr Mubarak is coming under increasing international pressure to resign, with the US now calling for an immediate transition of power.
But he has so far refused to go, saying doing so would leave Egypt in chaos.
In his first interview since anti-government protests began, he told ABC News he was "fed up" with power and would like to resign immediately.
But he repeated his long-held assertion that the country's Islamist opposition - the Muslim Brotherhood - would fill the power vacuum left by his absence.
The protest organisers are demanding that he leave immediately and have said they plan to march on the presidential palace on Friday.
They have been angered further by the emergence in recent days of pro-Mubarak gangs - many of them plain clothes police - who have attacked anti-government protesters.
The protesters have called on tens of thousands of people to gather in the capital after Friday prayers "so that we can put the last nail in the regime's coffin, and declare the victory of the 25 Jan revolution".
'Meaningful transition'
Egypt's Vice President Omar Suleiman has appealed for calm and urged the protesters to accept Mr Mubarak's pledge that he will not stand for election again.
But it has now emerged that the White House has been in talks with Mr Suleiman about how Egypt can begin making a "meaningful transition" to a democratic government that addresses the aspirations of the Egyptian people.
US Vice-President Joe Biden spoke to his counterpart Mr Suleiman on Thursday, say diplomats, a day Mr Suleiman had similar talks with Secretary of State Hillary Clinton.
The New York Times suggested that among the proposals was a plan for Mr Mubarak to resign immediately and hand power to a military-backed interim government under Mr Suleiman.
Neither the White House nor the State Department have directly denied the report.
But a spokesman for the President Barack Obama's National Security Council said it was "time to begin a peaceful, orderly and meaningful transition, with credible, inclusive negotiations".
"We have discussed with the Egyptians a variety of different ways to move that process forward, but all of those decisions must be made by the Egyptian people," said Tommy Vietor.
The BBC's Mark Mardell in Washington says other reports suggest the US plan has already been rebuffed in Egypt, and that the administration has been surprised by the attitude of the military and Mr Suleiman.
The reports say Mr Suleiman was aware of campaign in recent days to intimidate the opposition, and are now wondering whether he is the right man to lead an interim government, says our correspondent.
'Outrageous' violence
The crisis in Egypt has intensified in recent days as supporters of Mr Mubarak have begun attacking protesters in the capital.
Stones were thrown on both sides, and there were reports of gunfire, while footage has emerged of vehicles being driven at speed through crowds of protesters.
Foreign journalists reporting for several organisations have been attacked, with Mubarak supporters reported to have stormed a number of Cairo hotels.
The army, which has said the protests are legitimate, has been trying to keep the two sides apart but appeared to have failed to control the crowds.
Late in the evening, a number of political activists were arrested by military police, as were representatives of Human Rights Watch and Amnesty International.
Tens of thousands of people remained in central Cairo after dark on Thursday, some involved in running battles with Mubarak supporters.
The attacks have drawn condemnation from Britain, France, Germany, Italy and Spain, as well as UN Secretary General Ban Ki-moon.
"Let me be totally clear: this is outrageous and totally unacceptable, it must stop now," Mr Ban said.
In an interview with ABC News on Thursday, Mr Mubarak denied that his administration was behind the violence of the last two days but said it had troubled him.
He said he would like to stand down but that the country would be left in chaos if he did - a situation he said would be exploited by the Islamist Muslim Brotherhood.
The BBC's Kevin Connolly in Cairo said very few Egyptian will accept that version of events.
But the interview that gave is a fascinating insight into what is going on in the president's mind as he surveys the chaos in the capital, says our correspondent.
Source: BBC
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