Erdogan received the Doha-based Hamas leader Khaled Meshaal, whose group rules the Gaza Strip, at the Ottoman-era Yildiz Palace in Istanbul, the official Anadolu Agency reported, quoting presidential sources.
Turkish press reports have said Israel and Turkey could hold final talks on normalising ties on Sunday but this had yet to be confirmed.
Turkish Foreign Minister Mevlut Cavusoglu said on Thursday there was a "large possibility" the negotiations would take place by the end of this month.
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Anadolu said Erdogan and Meshaal discussed how to ease the humanitarian problems of the Palestinians and how to bridge the differences between Hamas and the other main Palestinian group Fatah.
The report made no reference to the Turkish talks with Israel.
Previously tight relations between Israel and key NATO member Turkey were significantly downgraded after Israeli commandos staged a deadly pre-dawn raid on a six-ship flotilla in May 2010 as it tried to run the blockade on Gaza.
Two of Turkey's key conditions for normalisation -- an apology and compensation -- were largely met, leaving its third demand, that Israel lift its blockade on the Hamas-run Gaza Strip, as the main obstacle.
According to the Hurriyet daily, a compromise has been reached with Turkey set to send aid for Palestinians via the Israeli port of Ashdod rather than sending it directly to Gaza.