At the forum Erdogan also pushed for the Israeli blockade of Gaza to end.
"Peace and stability will not come to the region as long as the blockade of Gaza persists.
"Painful experience has made it clear that no [regional] country will fully achieve prosperity and security as long as the Palestinian-Israeli conflict remains unresolved," he said.
Erdogan's call was echoed by many Arab leaders.
Saad al-Hariri, Lebanon's prime minister, said the Middle East was suffering under Israel's "criminal and barbaric'' attitude.
"We support Turkey's demands not only about the international investigation, but for Israel to apologise."
Ahmed Aboul Gheit, Egypt's foreign minister, said: "We support Turkey's demand to try those behind these acts."
During the forum, Turkey Syria, Jordan and Lebanon, said they would set up a council to create "a zone of free movement of goods and persons'' among them, and urged others to join what Ahmet Davutoglu, Turkey's foreign minister, said should not be seen as an alternative to the European Union.
Erdogan said Turkey was still eager to join the EU, but that the bloc "cannot and should not restrict [Turkey's] relations with its neighbours.''
Turkey has strengthened its ties with its Arab neighbours by mediating several conflicts, and cultivating new relationships with former rivals such as Syria and Iran,
forging free trade zones and gradually lifting mutual visa requirements.
The economic forum, set up in 2007, aims to build on a trade volume that
soared to $29bn last year between Turkey and Arab League countries, from $13bn in 2004.
Turkey already has free-trade agreements with Egypt, Jordan, Morocco, Syria, Palestinian territories and Tunisia, and is negotiating similar deals with Lebanon and Libya.
Turkey also lifted entry visa requirements for Jordanians, Libyans, Syrians and Lebanese and would like to extend "the free-trade and visa-free zone'' to other countries in the region, Erdogan said.