The decree has allowed a four-and-a-half month period for any amendments to the former constitution, which was suspended after the overthrow of the country’s former president, Mohammed Morsi, amid mass protests.
A presidential election will be held after the new legislative chamber’s first meeting.
The text of Mansour’s decree states that a panel for the review of the new constitution must be formed within 15 days.
In the run-up to parliamentary elections, the document also gives the interim president powers to issue new laws after consulting with the new government, which is to be formed soon.
Since last week, Egypt has been the scene of rival rallies and clashes between thousands of supporters and opponents of the ousted president.
Morsi is reportedly being held “preventively” by the military. Senior army officials say he might face formal charges over accusations made by his opponents.
Several arrest warrants have been issued for the members of Muslim Brotherhood.
Egyptian troops and security forces have recently expanded their roundup of top political figures from Muslim Brotherhood that had fielded Morsi for office.