was expected to join the US president to dine at the same table after the opening of the United Nations General Assembly in New York.
But the Turkish leader refused to sit at the table after walking into the room and seeing Trump was joined by President Sisi, Turkish media reported.
Erdogan has been an outspoken critic of the Egyptian president's rule since he seized power from the country's first democratically elected president in a 2013 coup.
Turkey's government was a key ally
of the short-lived administration of former President Mohammad al-Morsi.
Sisi's toppling and detention of Morsi, his subsequent labelling of the Muslim Brotherhood
as a terrorist group, and the massacre of more than a 1,000 pro-Morsi demonstrators in 2013 marked the Egyptian president as a key regional rival for Erdogan, alongside his Saudi and Emirati backers.
president earlier this year urged the UN to launch an investigation into the "suspicious" death of Morsi in prison.
The ousted president collapsed
and died in court in June this year.
Sisi's table-mate Trump
, however, has been outspoken in his support for the Egyptian president.
Trump has previously referred to Sisi
as his "favourite dictator
In a meeting on the sidelines of the UN General Assembly, Trump shrugged of protests against the rule of his "friend".
"Everybody has demonstrations," he said. "No, I'm not concerned with it. Egypt
has a great leader. He's highly respected."
Cairo's Foreign Ministry slammed the Turkish leader in response to the incident, accusing Erdogan of "sponsoring terrorism" in Syria
and making his country a "safe haven" for the Muslim Brotherhood.
Ministry Spokesman Ahmed Hafez pointed to thousands of "political prisoners" held in Turkish prisons.
"Scores [of] prisoners [have] died due to dubious circumstances, torture, and illness as a result of the maltreatment inside Turkish prisons," he claimed, adding that thousands of academics and government employees had been "arbitrarily" fired for alleged links to a 2016 coup attempt.
Hafez also acknowledged Ankara's status as the world's leading jailer of journalists
Critics of Egypt will no doubt consider the foreign ministry spokesman's comments ironic.
Cairo is one of the world's leading jailers of journalists, with at least 25 currently detained in Egypt, according to the Committee to Protect Journalists (CPJ).
Prison conditions in the country are also notoriously horrendous, with human rights organisations alleging that torture and the extended use of solitary confinement are rife in Egyptian prisons.
Cairo has also been accused of denying medical care and visits by family members and lawyers to political prisoners.
Protests sweep Egypt
Unprecedented demonstrations calling for the ousting of Sisi erupted last week in Cairo, Suez and other Egyptian cities.
The protests were sparked by corruption allegations lodged against Sisi, his wife and the military by a former government contracter, now self-exiled in Spain.
Mohamed Ali has accused Sisi and his military of appropriating millions of dollars in public funds to build a colossal presidential palace and a number of luxurious villas.
At least 1,300 people have been detained since Friday in what has been dubbed the "Palacegate" revolution, according to the Egyptian Center for Economic and Social Rights.
Egypt's prosecution sentenced nine people to 15 days in prison on Monday over their participation in the protests.
Among the sentenced was award-winning human rights lawyer Mahinour El-Massry
, who was arrested
on Sunday after attending an investigation of several of those arrested during the demonstrations.
As the Egyptian president prepared to speak at the United Nations General Assembly in New York on Tuesday afternoon, #NotMyPresident and #SisiLies ranked as top trends on Twitter in Egypt.
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