Nabil Fahmy sought to assure the world that the temporary government is following a road map that will see nationwide elections by next spring.
"It has so far succeeded in establishing the principles of justice, freedom and democracy as a basis for governance," said Fahmy, who is part of the temporary government established by Egypt's military following Morsy's ouster.
"This will be followed by parliamentary elections, then presidential elections, so that the transitional phase ends by next spring."
Fahmy's statement to the world body comes amid concerns that the military-backed government has been moving to outlaw the Muslim Brotherhood, the Islamist group that rose to power following the overthrow of Hosni Mubarak in 2011.
Western nations, including the United States and Britain, have urged Egypt's military-backed government to have an inclusive political process.
All Egyptians may participate in the political process, Fahmy said, "as long as they are committed to the renunciation of violence and terrorism and acts of incitement to them," and follow the rule of law.
The government is also determined to empower women and support its youth, Fahmy said.
Hundreds of Muslim Brotherhood supporters have been killed and thousands more have been injured in clashes with the military and its supporters following the ouster of Morsy.
Each side blames the other for stoking the violence.
Morsy, who was backed the Muslim Brotherhood's political arm, was the country's first democratically elected president.
But critics say he became increasingly authoritarian and forced through a conservative Islamist agenda during his year in power that alienated moderates.
He is also blamed for failing to revive Egypt's economy, which crashed when the 2011 uprising drove tourists away.
Just a year into his presidency, there were mass demonstrations calling for his removal.
After the Morsy ouster, Egypt's military began to crack down on his party, the Muslim Brotherhood. The crackdown led to ferocious clashes in the streets of Cairo and other Egyptian cities, many of which have led to condemnation from the international community.
Morsy, who was deposed by the military amid widespread protest over his rule, has been held in detention since early July.
Less than a block away from where Fahmy spoke at the United Nations, dueling protests took place between Egyptians who support the government and those who back Morsy.
"Free, free Egypt! Long live Egypt!" shouted the pro-Morsy crowd, some of whom waved pictures of the ousted president. One placard read, "Only in Egypt your vote never counts" and another read, "No to massacre and martial law in Egypt."
Nearby were those who support the current government. As they chanted "We love Egypt," one person raised a sign saying "Egyptians support our government in their war against terrorism."