Erdoğan's comments follow a year in which Turkey has taken steps to improve relations with a host of regional rivals.
Turkey's relations with Israel entered a deep freeze after the death of 10 civilians in an Israeli raid on a Turkish flotilla destined for the Gaza Strip in 2010.
Israel and a group of countries, including Turkey's historic rival Greece, then began work on a joint pipeline to bring eastern Mediterranean Sea gas to Europe.
Turkey strongly opposed the project and staked its own territorial claims on the region's energy wealth.
Erdoğan said he was resurrecting talks with Israel on an old idea to bring Mediterranean gas to European clients via Turkey.
"We can still do that," Erdoğan said.
"We are now holding talks with President (Isaac) Herzog. He could visit us in Turkey. Prime Minister (Naftali) Bennett also has a positive approach," Erdoğan said.
"As Turkey, we will do our best to cooperate on a win-win basis," he added. "As politicians, we should not be there to fight but to live in peace."
