"I have carried out several dialogues with political groups, which saw a majority in favour of holding presidential elections first," Mansour said in a televised address. "And I have amended the roadmap to meet their demands."
A political roadmap, laid down after the army ousted Islamist president Mohamed Morsi in July last year, called for parliamentary elections first. But many political parties said they would not be ready for a legislative vote this spring.
Mansour did not announce a date for the vote, a task that falls to the High Elections Commission. It must be held no less than 90 days after the adoption of the new constitution earlier this month, which will require a ballot before mid-April.
Several legislative amendments to the law regulating exercise of political rights and elections are also expected in accordance with the provisions of the new constitution.
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The President also said he would increase the number of courts dealing with terrorism charges to "bring perpetrators to justice swiftly".
Egypt has witnessed a steep rise in violence, with blasts now a regular occurrence, since the army toppled Morsi of the Muslim Brotherhood amid mass rallies against his one year turbulent rule.
Security forces have blamed Islamist elements for a series of blasts and violence and intensified a crackdown on them.
The President's comments came after 49 people were killed and 247 injured in violence on the third anniversary of the 2011 uprising which ended the three-decade-long autocratic regime of Hosni Mubarak.