Erdogan also said UN Secretary General Ban Ki-moon phoned him on February 2 to ask him to continue Turkey's role as a Middle East mediator.
During a panel discussion in Davos, Switzerland, on January 30, Erdogan accused Shimon Peres of "knowing very well how to kill," then stormed off the stage. The panel discussion on the Israeli offensive in Gaza also included Ban and the Arab League's Amr Moussa.
"If a demand arises from the parties, we again would shoulder this mission" of mediation, Erdogan told members of his party in parliament on February 3.
"The role of mediation does not prevent us from telling the truth. We don't voice our criticisms only to Israel, we tell every side, including Hamas."
Turkey, a predominantly non-Arab Muslim country that belongs to NATO, has close military and commercial ties with Israel. It has also helped negotiate a Hamas-led ceasefire that ended the rocket attacks that Israel said forced it to launch the incursion into Gaza in December.
Turkey has also led indirect talks between Israel and Syria and sent peacekeeping troops to southern Lebanon.
Crowds demonstrated in the Gaza Strip in support of Erdogan's comments to Peres, and thousands also cheered him in Istanbul upon his return from Davos.
Some 1,300 Palestinians died in Israel's month-long attack on the Gaza Strip. Israel lost 10 soldiers and three civilians.
Anger At Israel
Turkish Prime Minister Recep Tayyip Erdogan stormed out of a debate with Israeli President Shimon Peres at the World Economic Forum in Davos, Switzerland. He was later welcomed by cheering supporters when he returned home to Istanbul. Video By Reuters. Play