Confounding reports that he was planning to hand over power to his Vice President Omar Suleiman, a grim-looking 82-year-old Mubarak in a televised address said, "I will not accept to listen to matters dictated by countries abroad."
"I will remain adamant to shoulder my responsibility, protecting the constitution and safeguarding the interests of Egyptians (until the next elections)," he said, ignoring US President Barack Obama''s suggestion to start the process of transition "now."
Shortly after his speech, there were reports that he had left the country for an unknown destination. But there was no official word on it.
Expressing disappointment over Mubarak''s announcement, Obama asked the Egyptian leader to explain in "clear and unambiguous language the step by step process that will lead to democracy in the country."
"The Egyptian people have been told that there was a transition of authority, but it is not yet clear that this transition is immediate, meaningful or sufficient," he said.
Reacting angrily to Mubarak''s refusal to quit, thousands of anti-government protesters at the Tahrir Square took off their shoes and waved them at a giant TV screen showing his speech, shouting "Leave, leave!"
''Down with Mubarak'', they chanted as hopes about Mubarak''s resignation had run high after the military leadership had announced hours earlier that it would step in to ensure the country''s security and see that the people''s "legitimate" demands were met.
The build up for a celebrations turned into one of despair and widespread anger.
The protesters were planning to march to the heavily guarded presidential palace after the Friday prayers amid reports that Mubarak has flown out of the country.
Iranian state-run Press TV quoted Egyptian Presidential sources as saying that Mubarak has left the country and that his address was taped.
US-based Al-Hurra TV reported that Mubarak had left for the United Arab Emirates.
Pro-democracy protesters have been demanding an end to Mubarak''s 30-year rule since January 25. The protesters are angry over his autocratic rule, rising unemployment, high food prices and police brutality.
There was no indication in Mubarak''s speech that he was planning to step down any time soon.
"I said I would not run again for president. I also said I would go ahead with my responsibility of protecting the constitution and the people until they elect a new president in next September. This is what I have sworn to do and will keep it to take Egypt to safety," he said.
"I have decided to delegate power to the vice president (Omar Suleiman) based on the constitution," Mubarak said, adding he had requested six articles of the constitution to be amended and one article to be cancelled.
Mubarak said the current "moment was not against my personality, against Hosni Mubarak", and concluded by saying that he would not leave Egyptian soil until he was "buried under it".
Shortly after Mubarak''s speech, Suleiman called on protesters to "go back home" and "go back to work".
Suleiman said he had been delegated by the president "the responsibilities to safeguard the stability of Egypt, to safeguard its ... assets ... to restore peace and security to the Egyptian public, and to restore the normal way of life".
He said that steps had to be taken to "safeguard the revolution of the youth", but also called for protesters to "join hands" with the government, rather than risk "chaos", Al Jazeera reported.
Egyptian Ambassador to the US Sameh Shoukry said Suleiman was now the "de facto head of state".
"President Mubarak has transferred the powers of the presidency to his vice president, who now undertakes all authorities as president. So we can say that the President is a de-jure president, and the Vice President is the de-facto president," Shoukry told CNN.