The official spokesman of the Egyptian Ministry of Foreign Affairs Badr Abdel-Atti told Anadolu Agency (AA) that Amr had done everything he could and it was time to assign his duty to other officials.
Amr held a phone conversation with US Secretary of State John Kerry on July 5 and said, Morsi's forced departure was not a military coup.
"I hope that they read the situation in the right way, that this is not a military coup in any way," said Amr.
"The army is responsible for the security of the country and its people. The roadmap of the Egyptian army was determined by all the political blocs," Amr also said.
In a phone call with UN Secretary General Ban Ki-moon Thursday, Amr said Egypt is keen on "building a real democracy that guarantees the participation of all political groups without exclusion".
The roadmap agreed upon with political groups will be implemented swiftly, foreign ministry spokesman Abdel-Atti said in a statement.
The army unveiled a roadmap for Egypt's future on July 3, after the overthrow of elected President Mohammad Morsi.
Egypt has been thrown into political turmoil in the wake of Morsi's removal from power.
Hundreds of thousands of Morsi supporters have camped in the streets to demand the return of the Islamist president to power.
The demonstrators have been staging protests across Egypt to call for early presidential election.
Armed men fired at military checkpoint in Al-Arish
Unidentified armed men opened fire at a military checkpoint in Al-Arish in Egypt’s North Sinai on Saturday.
22 different places in the region were attacked in last week and 12 people were killed.