But frequent Turkish criticism of Israel's offensive in Palestinian-ruled Gaza a year ago has strained ties and last week Turkey's ambassador was publicly humiliated by the Israeli deputy foreign minister - an incident for which Ankara demanded and got an apology.
"The aim of the visit is to warm up bilateral relations. The Isareli-Turkey alliance is of mutual strategic importance," an aide to Barak said. Barak, a former army general and Israeli premier, met Davutoglu on Sunday after visiting the tomb of Mustafa Kemal Ataturk, the founder of modern Turkey. Neither party issued a statement afterwards.
Barak is also scheduled to meet the Turkish defence minister and hold a news conference later in the day. Absent among the hosts of the day-long visit was Turkish Prime Minister Tayyip Erdogan, whose AK Party's roots lie in political Islam and whose public fury at the hundreds of civilian dead in Gaza left Israel especially aggrieved.
Turkey barred Israel from participating in a Nato war exercise late last year because of its public's concerns over the Gaza offensive, which Israel says was launched to stop Hamas rocket attacks. Erdogan has since held high level meetings with the presidents of Syria and Iran, foes of Israel. Turkey's tilt toward Tehran has been watched with worry by Washington, which is at loggerheads with the Islamic republic over its nuclear programme. Israel sees the prospect of an Iranian bomb as a threat.