"Yes there is a crisis but we are on the right path and I believe in the future," he said after talks with his Sudanese counterpart Ali Karti.
Fahmy said Egypt would push ahead with its "roadmap", an army-drafted plan providing for elections in 2014.
"Our top priority is the national security of Egypt," the minister said.
"The coming Egyptian political system will be a democratic, open regime and open to all according to constitutional rules that will be written soon."
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A former ambassador to Washington, Fahmy was sworn in as part of an interim government after the Egyptian military toppled the country's Islamist president Mohamed Morsi on July 3.
The ouster of Morsi, a former Muslim Brotherhood leader who became his country's first elected president, followed popular mass protests calling for his resignation.
But almost 800 people have died in Egypt since last Wednesday when security forces moved to disperse two Cairo protest camps of Morsi's supporters, drawing global condemnation including from Sudan whose government calls itself Islamist.
Such attacks, said Fahmy, "confirmed that there is a plan to spread fear among Egyptian citizens and to shake Egypt.
"We will not allow anyone to make Egyptians fearful."
Fahmy said his regime wants to clarify the situation for its neighbours "especially Sudan", which Egypt and Britain jointly ruled until 1956.
"We came here with a clear political message: We want cooperation for the interests of the countries."
Fahmy left Sudan immediately after his talks with Karti.
Khalid Tijani, a Sudanese analyst, said he understood the visit had been planned ahead of the Egyptian crackdown, as part of efforts to reassure Sudan's neighbours after the change of regime.