Yahya Sinwar, Hamas's Gaza chief, has yet to make his response known, further complicating the situation.
Pressure has been mounting on Israel and Hamas to come to an agreement before Israel begins the latest military operation in Rafah.
Erdogan met Hamas leader Haniyeh to discuss Gaza aid and regional peace amid tensions with Israel. They emphasized support for Palestine and called for unity.
Earlier this week, as mentioned, the Prime Minister of Qatar, Muhammad al-Thani, announced that his country is "re-examining its position as a mediator between Israel and Gaza."