Barak later met Vecdi Gonuk, his Turkish counterpart, for talks on a nearly $180m arms deal.
Turkish officials are currently in Israel to test unmanned drone aircraft that Israeli companies have manufactured for Turkey's army.
The project has been long delayed over technical problems and political tensions.
Barak's one-day trip is the highest-level bilateral visit since a diplomatic feud erupted over Israel's recent treatment of the Turkish ambassador.
Danny Ayalon, Israel's deputy foreign minister, embarrassed Oguz Celikkol, the Turkish envoy, on Monday, making him sit on a low couch and removing the Turkish flag from a table in a meeting called to convey Israeli protests over a Turkish television series.
Israel later issued a formal apology, which Turkey accepted.
Barak's visit was scheduled before the incident, but the row was the latest in a series of disputes between the two nations.
Azzam Tamimi, a Palestinian author and political analyst who covers the policies of the current Turkish government, said Israel felt the need to apologise to prevent itself from losing Turkey as an important ally in the region.
"There were expectations that the whole visit would be called off, but because the Israelis did apologise, then the visit was made," Tamimi told Al Jazeera.
"It is no secret that within Turkey there is a division. There is the army and the defence ministry on one side, and the ruling party on the other side.
"The ruling party would want to proceed in a different unconventional direction, but they cannot do this unless they get the entire establishment behind them, and the army and the defence ministry are very closely associated with Israel."
Criticism over Gaza
Turkey, as a Muslim state, had been an important ally of Israel. But relations have soured following strong criticism by Recep Tayyip Erdogan, the Turkish prime minister, of Israel's war in the Gaza Strip last year.
Erdogan also angered Israel this month when he accused it of being a threat to world peace.
A Turkish television drama, The Valley of the Wolves, which depicts Israeli security forces as kidnapping children and shooting old men, has added to the hostilities.
That followed a drama aired on Turkish state television last October that portrayed Israeli soldiers shooting a Palestinian baby at close range.
Israel has said the programmes are anti-Semitic and inflammatory.