The row had threatened to break relations between Turkey and Israel
Israel's defence minister has held talks in Turkey, in the wake of a diplomatic row which has further soured relations between the two countries.
Ehud Barak said the public humiliation of Turkey's ambassador by an Israeli minister last week was a "mistake".
Turkish PM Recep Tayyip Erdogan, who did not meet Mr Barak, said Turkey would not take the issue further.
Israeli-Turkish relations have deteriorated since Turkey condemned Israel's Gaza offensive in 2008-09.
Despite the spat, Mr Barak was warmly greeted by Turkish military officials on his arrival in the capital, Ankara.
Among those welcoming the defence minister was the Turkish ambassador to Israel, Oguz Celikkol, whose dressing down by Israeli Deputy Foreign Minister Danny Ayalon came close to breaking relations between the two countries.
Mr Celikkol was pictured in the foreign ministry seated on a lower chair, the Turkish flag removed from the table.
He was rebuked over a Turkish television drama, which depicted Israeli intelligence agents kidnapping Turkish children.
The Turkish envoy was pictured seated lower than Israel's deputy minister [Image: Lior Mizrahi/Israel Hayom]
Mr Ayalon apologised after Turkey's president threatened to recall the ambassador.
"I believe it was a mistake, and the right step was taken according to the norms of diplomacy," Mr Barak said during his visit.
"It is appropriate that all the ups and downs in our relationship over the years should be solved and put behind us."
In what some analysts interpreted as a cold response by Turkey, Defence Minister Vecdi Gonul said the two nations would maintain relations as "strategic allies as long as our interests force us to do so".
He did not address the spat directly.
Mr Erdogan did not meet Mr Barak, but said in a news conference that it was clear that Mr Ayalon had "overstepped his mark".
"What is valid for us is Ehud Barak's statement here, in which he... accepted the mistake," Mr Erdogan said.
He said Turkey was "not thinking of taking the matter any further".
Relations between Israel and secular Muslim Turkey, already frayed, sharply deteriorated after Mr Erdogan repeatedly condemned Israel's Gaza offensive.
The BBC's Jonathan Head in Istanbul says political relations are still very strained, but there are surprisingly strong links between the two countries' military establishments, dating back to a co-operation agreement in 1996.
Mr Barak was expected during the visit to finalise details of a long-planned sale of Israeli-made unmanned aircraft to Turkey.
But, our correspondent says, the governing party in Turkey, with its staunchly Muslim power-base, has made it clear that the close ties the two countries once had are no longer a priority.