The major question is whether the stepped-up diplomatic pace will yield progress either on the stalled Israeli-Palestinian peace process or on Syria, where Mr. Kerry’s push to change President Bashar al-Assad’s “calculation” about his ability to hang on to power has yet to bear fruit.

Diplomatic ties between Turkey and Israel have been frozen since 2010, when nine activists — eight Turks and one American of Turkish descent — were killed when the Israeli military intercepted the Mavi Marmara, a Turkish ship that was trying to run the naval blockade on supplies to Gaza, and met resistance on board.

During his visit to Jerusalem last month, President Obama brokered an agreement between Israel and Turkey to restore ties. But no sooner had the agreement been announced than Turkey’s prime minister, Recep Tayyip Erdogan, boasted that it underscored his nation’s regional clout, adding to American concerns that the two sides might not follow through.

Several Israeli diplomats, including two senior advisers to the Israeli prime minister, Benjamin Netanyahu, were expected to arrive on Thursday in Ankara, the Turkish capital, to discuss the compensation Israel is expected to provide to the families of those killed in the 2010 episode.

Eager to smooth the path for a restoration of ties that would lead to the return of Turkish and Israeli ambassadors to their posts, Mr. Kerry said that he had been assured by Mr. Davutoglu that the Turkish government would avoid any boastful displays of “triumphalism” in having succeeded in getting the Israelis to make concessions — which included an apology from Mr. Netanyahu.