US Secretary of State John Kerry on Sunday called on Turkey and Israel to fully normalise their ties, two weeks after the Jewish state's US-brokered apology for a deadly 2010 raid on a Gaza aid flotilla organised by a Turkish charity.

The top US diplomat also warned Iran that time is running out on nuclear negotiations between the Islamic republic and world powers.

"It is not for the United States to be setting conditions or terms," Kerry told a joint news conference with Turkish Foreign Minister Ahmet Davutoglu in Istanbul.

"We would like to see this relationship that is important to stability in the Middle East, critical to the peace process itself, we would like to see this relationship back on track in its full measure," he said.

"To be back on track in its full measure, it is imperative that the compensation component of the agreement be fulfilled, that the ambassadors be returned, and that that full relationship is embraced," Kerry said.

"I am confident that there will be goodwill on both sides."

Israel apologised to Ankara on March 22 for the deaths of nine Turkish activists in a botched raid by Israeli commandos on a Gaza-bound aid ship, in a breakthrough engineered by US President Barack Obama during a visit to Jerusalem.

The apology ended a nearly three-year rift between Israel and Turkey -- two key US allies in the region -- and the two countries are due to begin talks on compensation on Friday.

But they have yet to exchange ambassadors and fully restore diplomatic ties.

Turkish Prime Minister Recep Tayyip Erdogan accepted the apology "in the name of the Turkish people" but said the country's future relationship with Israel including the return of ambassadors would depend on the Jewish state.

The Israeli apology was cherished as a victory for Turkey in some quarters.

But Kerry noted: "The foreign minister expressed to me very clearly in response to any inquiry from me that they have taken steps to try to prevent any kind of triumphalism."

For his part, Davutoglu praised the efforts by Obama and Kerry to help reconcile the two Washington allies.

"Now it will be important to make progress in fulfilling the conditions by taking rational and principled steps," Davutoglu said.

"We have overcome the apology issue and now we'll hold talks about compensation," he added.

After talks in Turkey, Kerry heads later Sunday to Israel and Ramallah in the West Bank, where he will meet with Palestinian president Mahmud Abbas.

He will also meet with Israeli Prime Minister Benjamin Netanyahu on Monday, in what will be his third trip to the Middle East region since the start of his tenure on February 1.

-- Turkey could have 'profound impact' on Mideast peace --

US officials have said the return visit will give him a chance to probe possibilities for restarting the moribund peace process in the wake of Obama's trip last month.

Observers say the Turkish-Israeli rapprochement could enable Ankara to play a role in the Middle East peace process and in particular encourage reconciliation between rival Palestinian factions, Hamas and al-Fatah.

Davutoglu said he spoke by telephone late Saturday with Abbas and Khaled Meshaal, the re-elected head of the Islamist Hamas movement.

And Erdogan is expected to visit the United States for talks with Obama on May 16.

"Turkey can be a key, an important contributor to the process of peace in so many ways," Kerry said in Istanbul.

"I think in many, many respects a country as strong, and as vibrant as energised and as transformative as Turkey can have a profound impact by being a partner in this process," he added.

On Iran, Kerry warned that negotiations between world powers and the Islamic republic could not go on forever.

"This is not an endless process, this is not something where you can play with the clock. You can't just delay and talk for the sake of talking," he said.

Kerry said there had been hope that talks in the Kazakh capital Almaty might have helped to narrow differences between the two sides, adding: "But the door is still open for doing that."

Iran and six world powers -- the United States, Russia, China, Britain, France and Germany -- failed to break the deadlock over Tehran's nuclear drive after two days of talks in Almaty aimed at limiting Iran's nuclear programme.

Chief negotiator Catherine Ashton, the European Union's top diplomat, said Saturday that the sides were still "far apart" and no new date was agreed for the resumption of negotiations.

The continuing diplomatic deadlock comes as Israel refuses to rule out a pre-emptive strike targeting atomic facilities in the Islamic republic.

Kerry repeated Washington's desire for a diplomatic solution.

"We would repeat to Iran, it is our desire to have a diplomatic solution but this choice lies in the hands of the Iranians," he said.