Turkish and Israeli diplomats began talking, on Monday in Ankara, about compensation for the families of Turks killed when Israeli commandos raided the MV Mavi Marmara in 2010. Published reports suggested that Israel hopes to widen the talks, but Turkish officials, with an eye on domestic public opinion, appear determined to move slowly in rebuilding relations.
The US, meanwhile, is eager for a restoration of the relatively smooth bilateral ties that linked Turkey and Israel before the Mavi Marmara affair. John Kerry, the US secretary of state, pushed for rapid progress when he visited Turkey on April 7, but in reply Turkey abruptly postponed the compensation talks, which finally started this week.
Now the Turks have rebuffed the US again; Mr Kerry, back in Turkey on Sunday, proposed that the prime minister, Recep Tayyip Erdogan, scrap a plan to visit Gaza next month. Mr Kerry's stated concern is that such a visit would damage the prospect of revived Israel-Palestinian peace talks - a prospect, it must be said, that only Mr Kerry can detect right now.
The US bid to get Mr Erdogan to hold off on visiting Gaza brought a quick, terse reply from Bülent Arinç, the deputy PM, who called Mr Kerry's request "objectionable, wrong and incorrect".
Beyond all this posturing, however, healing the rift between Israel and Turkey soon would help both sides. There are, as we have noted here before, potent economic advantages in re-normalised relations. These include expanded trade, Turkish access to Israel's offshore natural gas and even tourism. Turkey used to attract many Israeli visitors.
Normal relations also offer political advantages, and on this front Palestinians, especially those in Gaza, may be the surest beneficiaries.
Turkey on better terms with Israel could be a capable broker between Israel and the Palestinians, starting by pushing Hamas towards a reconciliation with Fatah, a real step towards Mr Kerry's ideal of Palestinian-Israeli talks. For the moment, the Hamas-Fatah rift is so great that Palestinian President Mahmoud Abbas, who was in Istanbul yesterday, also opposes Mr Erdogan's visit to Gaza (though he has said Turkey can play a leading role in spearheading reconciliation).
To be sure, even the US has found little leverage to apply to Israel's current intransigent leadership and blockade of the Strip. But developing mutual interests - regionally first - is exactly the way to build leverage.