Barak is the first Israeli official to visit Turkey since the diplomatic feud that erupted Monday after Israel's deputy foreign minister, Danny Ayalon, summoned Turkish Ambassador Ahmet Oğuz Çelikkol to complain about a TV show. The ambassador was forced to sit on a low sofa without a handshake, while Ayalon explained to local TV stations that the humiliation was intentional. Outraged, Turkey threatened to recall the ambassador, forcing Ayalon to apologize.
The quarrel was the latest in a series of disputes between allies who had built strong military and economic ties over the past 15 years.
The visit was scheduled before the row, but is being closely watched for efforts to control the damage to the relationship that has also been hurt by Turkish Prime Minister Recep Tayyip Erdoğan's frequent outbursts of fury over what he considers Israel's aggressive treatment of Palestinians.
Hours before Barak's departure, Ayalon said the Turkish ambassador could be expelled if Turkish TV dramas continue to depict Israeli security forces as brutal. Ayalon had called in the ambassador to reprimand him over a TV program that showed Israeli agents kidnapping children and shooting old men. It was the second such program to be aired on Turkish television in recent months.
Barak on Sunday met with Turkey's Foreign Minister Ahmet Davutoğlu to discuss the latest crisis. He is also scheduled to meet Turkish Defense Minister Vecdi Gönül later Sunday.
Barak and his fellow Labor Party member, Minister Binyamin Ben Eliezer, have significantly warmer relations with Turkey than Ayalon and Foreign Minister Avigdor Lieberman's ultra-nationalist party.
Upon his arrival in Turkey, Barak was greeted warmly at the airport by a Turkish admiral. His first stop was at the mausoleum of modern and secular Turkey's founder, Mustafa Kemal Atatürk, whom Barak praised as an inspiration in making the region "one of peace and security."
Although there are ongoing military cooperation projects between Turkey and Israel, such as the purchase from Israel of Israeli-made Heron unmanned aircraft, the level of cooperation has decreased.
Barak was expected to discuss the US$190 million (131 million euros) deal for the Herons, which was signed several years ago, but which has been held up due to a malfunction in a camera system manufactured for the drones by a Turkish subcontractor.