Despite mounting global clamour for him to step down immediately, 82-year-old Mubarak, who has been in power since 1981, refused to bow to the pressure.
Seeking immediate start of an "orderly transition" in Egypt, US President Barack Obama expressed hope that Mubarak would be able to make the "right decision".
"In order for Egypt to have a bright future, the only thing that will work is moving an orderly transition process that begins right now that engages all parties, leads to democratic practices, fair and free elections and a representative government that is responsive to the grievances of the Egyptian people," Obama said in Washington.
EU leaders, at a summit in Brussels of the 27-nation bloc, said Egypt's "transition process must start now" and condemned this week's violence. Egypt's new Vice President Suleiman and other top military leaders were discussing steps to limit Mubarak's executive powers and possibly remove him from the presidential palace in Cairo — though not to strip him of his presidency immediately, Egyptian and American officials were quoted as saying by The New York Times.
A transitional government headed by Suleiman would then negotiate with opposition figures to amend Egypt's Constitution and begin a process of democratic changes, it said, adding that among the ideas discussed were suggesting to Mubarak that he move to his home at Sharm el Sheik, the seaside resort, or embark on one of his annual medical leaves to Germany for an extended checkup.
"Such steps would provide him with a graceful exit and effectively remove him as the central political player, going partway toward addressing a central demand of protesters on the streets of Cairo," the report said, as hundreds of thousands of protesters packed Cairo's Tahrir (Liberation) Square last evening for a "day of departure" rally for Mubarak.
The Wall Street Journal also reported quoting people familiar with the matter that if these discussions bear fruit, "executive powers in the new government could be gradually transferred to Suleiman, the country's longtime intelligence chief, and a transition government that includes opposition figures."
Separately, the Washington Post said the Obama Administration is urgently trying to persuade opposition groups to participate in dialogue with Suleiman. The Obama administration, the daily said, has urged Egyptian military to back the dialogue.
"In conversations with Defence Minister Field Marshal Mohamed Tantawi and Lt Gen Sami Enan, the military chief, administration officials stressed the importance of preserving the army's position as the most respected institution in Egypt," the daily said.
In an interview to ABC News, his first since the revolt began last week, Mubarak said he is "fed up" and wants to quit but fears that the nation will "sink in chaos" if he steps down at this stage.
"I am fed up. After 62 years in public service, I have had enough. I want to go," said Mubarak.
"If I resign today, there will be chaos," he said when asked about today's deadline by the protesters for him to quit and leave the country. "I don't care what people say about me. Right now I care about my country."
He said he could have fled the country like other Presidents did but he refused to do so. He said he was present in the presidential palace with his son Gamal.
Mubarak, earlier in a speech in front of Parliament, vowed he will remain President "as long as his heart is beating." Meanwhile, Fox News reported that a failed assassination bid against Suleiman has left two of his bodyguards dead.
"Such an attempt on the life of Omar Suleiman would mark an alarming turn in the uprising against the government of President Hosni Mubarak, who only recently named Suleiman as Vice President in an effort to quell the unrest and possibly line up a successor," it said, without giving details.
White House Press Secretary Robert Gibbs, however, refused to comment on the issue.
"I am not going to... get into that question," he was quoted as saying. An Egyptian journalist died yesterday of gunshot wounds he received during violent clashes between pro-and anti-Mubarak demonstrators.
Ahmed Mohammed Mahmud of Al-Taawun newspaper published by the state-owned Al-Ahram foundation, who was in coma for four days, has died, local media reported. Mahmud was shot by sniper fire when he was taking pictures from his flat near Tahrir Square.
Mubarak has blamed opposition Muslim Brotherhood for the violence in Cairo and said "I was very unhappy (about violence)... I do not want to see Egyptians fighting each other."
Massive crowds yesterday thronged the Tahrir Square, the hub of unrelenting protests against Mubarak that have claimed over 300 lives in 12 days, for a "day of departure" rally against Mubarak, chanting slogans, bowing in prayer and waving national flags.