In a televised address, Mubarak said, "I say in all honesty and regardless of the current situation, that I did not intend to nominate myself for a new presidential term."
Making it clear that he was in no mood to give up power as of now, Mubarak said he would seek changes to the constitution and called on "parliament to discuss amendments to Articles 76 and 77 of the constitution to change the conditions for presidential candidacy and limit terms."
The next presidential election is scheduled for September. Until now, officials had indicated 82-year-old Mubarak would likely run for a sixth six-year term of office.
Mubarak also said he has no intentions of leaving Egypt. "This is my country. This is where I lived, I fought and defended its land, sovereignty and interests, and I will die on its soil," he said.
Shortly after his speech, clashes broke out between pro-Mubarak and anti-government groups in the Mediterranean city of Alexandria, Al Jazeera reported.
Stone-pelting youths at Alexandria`s Mahatit Masr Square scattered as automatic gunfire rang out and a tank advanced towards them before halting and then withdrawing.
There was no sign of any casualties, the channel said.
Mubarak`s words failed to convince over a million protesters gathered at the Cairo`s Tahrir Square. They resumed their "Leave, Mubarak!" chant shortly after his speech.
Tens of thousands of unrelenting protesters who had converged on the Tahrir Square chanted, "we won`t leave tomorrow, we won`t leave Thursday ...", in a clear message that they will continue their protest till Mubarak steps down.
The speech was Mubarak`s second direct address to the nation since the most serious challenge to his 30-year-rule began nine days ago.
Earlier on Saturday, he sacked his Cabinet, named a vice-president for the first time and promised economic and political reforms.
Unfazed by the countrywide protests, Mubarak in his fresh speech said that he will ensure a "peaceful transition of power" after elections due in September this year.
Watching his speech on a giant TV screens, protesters booed and shouted "Go Mubarak Go" and "Leave! Leave! Leave!"
The protesters jammed in shoulder-to-shoulder turning Tahrir Square into a sea of humanity in the "march of a million", after the powerful military showed signs of distancing itself from the besieged President vowing that it would not fire on the protesters.
At the beginning of his speech, Mubarak said that "the young people" have the right to peaceful demonstrations.
But his tone quickly turned accusatory, and he lashed out at his detractors saying the protesters had been "taken advantage of" by people trying to "undermine the government".
Mubarak`s address came as he virtually lost the backing of his strongest ally - the US - with President Barack Obama reportedly sending a message through an envoy to Mubarak not to run for another term.
Nobel peace prize winner and opposition leader Mohamed ElBaradei dismissed Mubarak`s speech as an "act of deception".
ElBaradei said if Mubarak did not heed the call to leave power at once, he would be "not only a lame-duck president but a dead man walking".
"He`s unfortunately going to extend the agony here for another six, seven months. He continues to polarise the country. He continues to get people even more angry and could (resort) to violence," he was quoted as saying by Al Jazeera.
The protests in Egypt erupted close on the heels of the events in Tunisia, where a popular uprising ended the 23-year-reign of Zine El-Abidine Ben Ali.