Speaking after talks with Turkish counterpart Vecdi Gonul, Barak said he was "more confident that certain ups and downs in our relationship could and should be corrected and we can continue to follow the tradition... of good and friendly cooperation and understanding."
Gonul said Turkey and Israel remained allies, but made it clear the partnership should not be taken for granted.
"We are allies, strategic allies, as long as our interests force us to do so," he said.
Barak "received no firm commitment that Turkey would tone down its criticism of Israel," an official from the Israeli delegation said on condition of anonymity.
"Time will tell" how ties will develop, he added.
Barak met also with Foreign Minister Ahmet Davutoglu, but Prime Minister Recep Tayyip Erdogan, a central figure in bilateral tensions, and President Abdullah Gul, were not available to meet him, citing programmes outside Ankara.
It was the highest-level bilateral visit since Israel's offensive on the Gaza Strip last year prompted an unprecedented barrage of criticism from Erdogan's Islamist-rooted government, marking a sharp downturn in relations.
Barak, whose Labour Party is in favour of keeping close ties with Turkey, insisted on the visit amid a row that brought Ankara to the verge of recalling its ambassador from Tel Aviv.
"Turkey is a very important country... a pillar in the region, and dialogue and cooperation with it are very important," Barak said.
Gonul voiced hope that cooperation in arms projects, which has been at the heart of the once-flourishing ties, would continue.
The long-delayed delivery of 10 unmanned aircraft manufactured in Israel for the Turkish army is expected to be completed by June, he said.
The latest diplomatic storm between the two countries broke Monday when Danny Ayalon, the deputy of Israel's ultra-nationalist Foreign Minister Avigdor Lieberman, gave Turkey's ambassador a public dressing down in a meeting called to protest a Turkish television series for showing Israel in bad light.
Addressing reporters in Hebrew, Ayalon told them to pay attention that the envoy was made to sit on a low couch and that the Turkish flag was removed from their table.
Bowing to pressure from a furious Ankara, Ayalon apologised Wednesday.
Bilateral ties have been already poisoned amid frequent Turkish outbursts over Israel's war on Gaza and its persisting blockade of the impoverished Palestinian enclave.
Erdogan stormed out of a debate at the World Economic Forum last year, accusing Israel of "barbarian" acts and telling its President Shimon Peres, sitting next to him, that "you know well how to kill people".
Ankara has said relations will continue to suffer unless Israel ends "the humanitarian tragedy" in Gaza and revives peace talks with the Palestinians.
In October, it excluded Israel from traditional joint air exercises in central Turkey, angering Tel Aviv and prompting a rebuke from Washington.
Turkey's blooming ties with Syria and close contacts with Iran have made its snubs even harder for Israel to swallow and raised questions on whether a key Muslim-majority NATO member is sliding away from the West.
Turkey became Israel's main regional ally when the two signed a military cooperation accord in 1996.
The pact eased Israel's isolation in a hostile Arab neighbourhood, while Turkey gained an ally against Syria, then an arch-foe for sheltering Kurdish rebel leader Abdullah Ocalan, and access to Israel's advanced military technology.
-----------------------------------------------------------------------------------------