Khatami's letter to each of the two found its way to the Iranian news agency (IRNA) Tuesday.
"The regrettable news of the (Palestinian) conflict hurts the heart of every Muslim and jeopardizes the identity of the 'fighting Palestinian', which has proved very effective over 60 years of resistance," said the letter.
"The bloodshed in Gaza, which was only recently freed from the Zionist occupation, and the events that followed, paint a sad picture of differences between brothers and sisters, whose house remains under siege.
"As part of my human, Muslim, capacity as Director of the International Institute for Intercultural and Civilization Dialogue, I ask that you strive to reach a ceasefire and bring this tragedy to its end.
"There is no doubt that the conquering regime (Israel) would use this tragic conflict to oppress the Palestinian people and further deprive them of their rights, in order to diminish the problems it faces in wake of the courageous resistance in Palestine and Lebanon," continued the letter.
Khatami went on to wish the Palestinians "a great victory… for all those who are fighting for the fulfillment of human rights."
He called on both Abbas and Haniyeh to start negotiations, offering to take an active part in any initiative that may resolve their differences.