Ties between Ankara and Cairo have been strained since then army chief Sisi toppled elected President Mohamed Mori of the Muslim Brotherhood last year after mass protests against his rule.
Egyptian security forces then mounted one of the fiercest crackdowns against the Islamist movement, killings hundreds of supporters at a Cairo protest camp, arresting thousands and putting Mori and other leaders on trial trial.
After world leaders gathered at the United Nations, Erdogan delivered a speech which featured stinging criticism of Sisi's rise and what he called inaction after Mori's overthrow.
"Again, those objecting (to) the murders in Iraq, Syria and the murder of democracy in Egypt are subjected to certain unfair and groundless accusations and almost immediately accused of supporting terrorism," said Erdogan.
"The United Nations as well as the democratic countries have done nothing but watch the events such as overthrowing the elected president in Egypt and the killings of thousands of innocent people who want to defend their choice. And the person who carried out this coup is being legitimized."
In a statement, Egypt's foreign ministry dismissed Erdogan's comments on Sisi.
"There is no doubt that the fabrication of such lies and fabrications are not something strange that comes from the Turkish President, who is keen to provoke chaos to sow divisions in the Middle East region through its support for groups and terrorist organizations," the foreign ministry said.
"Whether political support or funding or accommodation in order to harm the interests of the peoples of the region to achieve personal ambitions for the Turkish president and revive illusions of the past."
Erdogan's comments prompted Egyptian Foreign Minister Sameh Shukri to cancel a meeting on the sidelines of the General Assembly with his Turkish counterpart, according to the statement.
Mori's Muslim Brotherhood has close ties with Erdogan's AK Party and Turkey has emerged as one of the fiercest international critics of Mori's removal, calling it an "unacceptable coup" by the army.
"If we defend democracy, then let's respect the ballot box. If we will defend those who come to power not with democracy but with a coup then I wonder why this UN exists," Erdogan said in his speech.
Both the fall of the Muslim Brotherhood and the advance of Islamic State has drawn regional countries into sectarian and ideological conflicts destabilizing the Middle East.
Erdogan and Turkish Prime Minister Ahmet Davutoglu, architects of a foreign policy which envisages Sunni Muslim Turkey as a regional power, have been reluctant to engage in action they fear could strengthen their enemy, Syrian President Bashar al-Assad, and exacerbate sectarian tensions inside Iraq.
Ankara has backed Syrian rebel groups fighting Assad but strongly denies any suggestion that it has supported Islamic State or other radical Islamist militants, saying they pose a major security threat to Turkey.
Egypt has been at odds with both Turkey and Qatar over the political transformation in the biggest Arab country since a popular uprising toppled autocrat Hosni Mubarak in 2011.
Egypt says Sisi's removal of the Brotherhood was not a coup, arguing that he was responding to the will of the Egyptian people after they rejected his troubled one-year rule.
Saudi Arabia and the United Arab Emirates, Gulf Arab oil producers who feel threatened by the Brotherhood, have showered Egypt with billions of dollars since Mori's exit.
Sisi's opponents accuse him of returning Egypt to an authoritarian past with widespread human rights abuses.