Other top leaders resigned also, including “Gamal Mubarak, the son of Hosni Mubarak. The new secretary general of the party is Hossam Badrawi, seen as a member of the liberal wing of the party.”
Update 3: There seems to be some confusion now whether Hosni Mubarak did resign as head of the NDP. Al Jazeera deleted their update re: Hosni Mubarak’s resignation and the Los Angeles Times reports that Al Arabiya television retracted their story.
Update 2 (updated): per Al Jazeera, Mubarak claims he cannot resign as President because it would violate the Egyptian constitution.
the legal mechanisms for him to go are complicated under the constitution … he can say he can no longer lead and give it over to VP, The Arabist suggests.
I believe extra-constitutional means deserve to be considered to: suspend the current constitution and have a transition council, for instance.
Another path that would remain within the constitution is to use Article 139 to appoint more vice-presidents, each empowered to deal with various aspects of the situation: one to take the lead on constitutional reform, one to investigate the events of the past week, one to restore and reform the Ministry of Interior, etc. It would be a defacto Council of Wise Men (and hopefully at least one woman!)
Update 1: Earlier, the head of the army appeared in the square asking everyone to go home – and the army is trying to get the protesters to remove their barricades. More people are moving into the square according to Al Jazeera and there is concern that tonight’s curfew (in 30 minutes) will bring a military attempt to clear the square.
Having Mubarak announce his resignation as party head – but not as President – may well be an attempt for the government to say they have compromised and it’s now time to end this.