Relations between Ankara and Cairo took a nosedive after the Egyptian military deposed Morsi on July 30, 2013.
Morsi, a Muslim Brotherhood leader, had been a close ally of Turkish President Recep Tayyip Erdogan's ruling Justice and Development Party-led (AKP) government.
Erdogan repeatedly condemned the ouster as a "coup d'etat" against Morsi, and in a show of solidarity at rallies he has often flashed the four-finger "Rabaa" hand salute -- seen as a symbol of the Muslim Brotherhood.
However he sounded a note of caution that high-level relations would not be repaired overnight.
"We think we need to start from somewhere," he said.
It is not the first time Yildirim has expressed hope for improved relations with Egypt.
In June, he said he did not want to see "permanent enmity" with countries such as Egypt and Syria.
Regional powerhouse Saudi Arabia, one of the main backers of Egyptian President Abdel Fattah al-Sisi, is keen to see the two countries reconcile as it grows increasingly close to Turkey.
However, the foreign ministry released a statement on consular efforts to help Egyptians in Turkey.
Turkey appears to be taking steps to return to its former "zero problems with neighbours" foreign policy after rapprochements with Russia and Israel in June this year.
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