Addressing the newly-constituted Upper House of Parliament, Mursi said the country will witness a period of renaissance with the new constitution that has ended the transition period.
"All are equal before the law, and in this constitution," he said of the charter drawn up by an Islamist-dominated council and approved in a referendum, adding that there would be "freedom for all people, with no exceptions."
Mursi said that the Shura council or the Upper House holds now the country's legislative authority and played down the country's economic woes.
"General indicators for the social and economic situation have shown some noticeable progress," Morsi said.
Egypt adopted the Islamist-backed constitution after a two-thirds 'yes' vote in a polarising referendum in December.
Some 63 per cent backed the constitution in the referendum.
"By virtue of the constitution the transitional period has now ended," the Islamist president said.
After this new constitution, the country is going to witness a period of renaissance where all Egyptians have to unite, he said.
He denied the country is facing bankruptcy and said the economy was showing positive indices. He also denied Egypt will allow any country to interfere in its affairs nor will it interfere in the affairs of other countries.
He expected that the regime in Syria will not be able to survive the current situation and added that the security of the Arab Gulf is a collective responsibility of Arab states.