Petraeus, whose program was kept secret due to security concerns, was initially thought to be in İstanbul to discuss the deteriorating situation in Syria and the fight against the terrorist Kurdistan Workers' Party (PKK) with Turkish officials.

However, some Turkish columnists including Fehmi Koru and Eyüp Can have claimed that the main topic of the discussions was Turkish-Israeli relations. Petraeus flew to Israel after his one-day visit to İstanbul, the columnists claimed, to achieve his goal of helping to restore the relations.

The alliance between the Jewish state and Turkey, a mainstay of Washington's influence in an unstable region, fell apart after the Israeli military raid in May 2010 of the Mavi Marmara ship headed for the blockaded Gaza Strip carrying humanitarian aid, which killed eight Turkish citizens and one Turkish American.

Can, who writes for the Radikal daily, drew attention in his column on Thursday to the fact that Petraeus was accompanied during his İstanbul visit by US senators John McCain and Joseph Lieberman, who are known to be close to Israeli government.

In apparent support for these claims about the aim of Petraeus's visit, Israeli newspaper Yedioth Ahronoth said on Wednesday that the US was trying to mediate an end to the dispute, for which Turkey has set several demands including that Israel apologize for the Mavi Marmara deaths. Israel denied wrongdoing after the flotilla attack and offered statements of regret, rather than contrition.

Israeli and Turkish officials had no comment on the report. But Israel's foreign minister, Avigdor Lieberman, said on Tuesday he was open to taking a page from US diplomacy in crafting a statement to try to end an impasse with Ankara.

The foreign minister compared the Mavi Marmara incident to one in which the United States mistakenly killed 24 Pakistani soldiers in an air strike last November on the Afghan border. Following the strike, Secretary of State Hillary Clinton said her country was "sorry for the losses suffered by the Pakistani military" and that Washington was "committed to working closely with Pakistan and Afghanistan to prevent this from ever happening again.”

The foreign minister said Clinton's statement could not be termed an apology, but was rather “an expression of regret on the killing of innocents.”

"I say to you if this is the wording -- if the Turks accept the American wording -- I will certainly go with it. This is what I am willing to accept [in terms of an apology for the raid]," he told his party in a speech on Tuesday.

The signal from the minister was significant because he had been among the Israeli leaders most vocally opposed to accommodating the Turks' rapprochement demands.