The election follows the removal of President Hosni Mubarak in February after a popular revolt.
The Muslim Brotherhood ran candidates as independents in previous elections, to circumvent a ban on the group.
It has sought to allay fears of an Islamist parliamentary majority, and said it would be willing to co-operate with secular parties.
Mohammed al-Mursi, the head of the new Freedom and Justice Party, told reporters in Cairo: "It is not an Islamist party in the old understanding, it is not theocratic."
Egypt's constitution bans parties based on religion, class or regionalism.