"Israel has three paths ahead: It either apologises, or accepts the findings from an international commission investigating the raid, or Turkey will cut off ties," Davutoğlu told.
Once Israel's closest Muslim ally, Turkey has said several times it wants Israel to apologise over the May 31 raid, pay compensation, agree to a UN inquiry into the incident and lift the blockade of 1.6 million Palestinians living in Gaza Strip.
Turkey has said before it was reviewing ties with the Jewish state. But Davutoğlu's words are the first time Ankara has explicitly threatened to sever ties unless its demands are met.
Israel has opened its own inquiry.
Davutoğlu met Israel's Trade and Industry Minister Benjamin Ben-Eliezer last week in Brussels in talks aimed at mending fences. Turkey said then it had told Israel what it should do to repair ties.
"The messages conveyed to Ben-Eliezer have reached the Israeli government. We will not wait forever for an answer," Davutoğlu told.
"It will be enough if their own commission rules that the raid was unfair and they apologise in line with the commission's verdict, but we have to see the verdict first."
Nine Turkish pro-Palestinian activists were killed in international waters when Israeli commandos stormed the Turkish-flagged ship Mavi Marmara on May 31 to stop a relief aid flotilla headed for Israeli-blockaded Gaza.
Turkey withdrew its ambassador to Israel, cancelled joint military operations and barred Israeli military aircraft from Turkish airspace after the incident.
The United States wants Israel and Turkey, whose earlier friendship had benefited US policy in the Middle East, to patch up the dispute. President Barack Obama is due to meet Israel's Benjamin Netanyahu in Washington on Tuesday.
Relations between Israel and Turkey have been on a downward spiral since Prime Minister Tayyip Erdoğan spoke out forcefully against an Israeli offensive in Gaza at the end of 2008.
The two countries had forged a friendship in the 1990s largely based on military cooperation and intelligence sharing, though trade also prospered.
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