US Secretary of State John Kerry struggled to convince Turkey's leaders they should promptly restore full diplomatic ties with Israel, to help calm the turbulent Middle East.
Turkey demanded that Israel first end all commercial restrictions against the Palestinians before the once-close partners could end their estrangement.
The estrangement stems from an Israeli raid in 2010 on a flotilla bound for the Gaza Strip. Eight Turks and a Turkish-American died.
US president Barack Obama revived the rapprochement during a visit to Israel last month, and Kerry aimed to firm that up in Istanbul, the first stop in a 10-day trip.
The stakes are high, given that the US sees Turkey and Israel as anchors of stability in a region riven by Syria's civil war.
Concern is also voiced over Arab Spring political upheavals and the potential threat posed by Iran's nuclear program.
Mr Kerry urged that promises of "compensation be fulfilled, ambassadors be returned and that full relationship be embraced."
He also met with Prime Minister Recep Tayyip Erdogan and then went to Israel.
Mr Obama, before leaving Israel two weeks ago, arranged a telephone conversation between Israeli Prime Minister Benjamin Netanyahu and Erdogan.
Mr Netanyahu apologised for the flotilla incident; compensation talks are expected to begin this week.
But Mr Davutoglu suggested that full normalization of ties would probably take some time.
He signalled that Turkey would pursue a "careful" advance toward a complete restoration of relations, with compensation and an end to Israeli trade restrictions on Gaza as the stumbling blocks.
Fixing the relationship long has been a goal of the Obama administration.
The US desperately wants significant progress by the time Mr Erdogan visits the White House in mid-May.
The Turks have billboards in Ankara celebrating Mr Netanyahu's apology and praising Mr Erdogan for bringing pride to his country.
From a US strategic sense, cooperation between the American allies has become more important as Syria's two-year conflict has grown ever deadlier.
More than 70,000 people have died in the war, according to the United Nations.