US Vice President Joe Biden on Sunday wrapped up a key visit to Turkey without a breakthrough on military cooperation in the Syrian crisis but with officials confident the talks brought their positions closer.

During his three-day trip to Istanbul, Biden held several hours of talks with both Turkish President Recep Tayyip Erdogan and Prime Minister Ahmet Davutoglu on the crises created by the capture by Islamic State (IS) jihadists of swathes of Iraq and Syria.

Washington has been frustrated by the relative lack of support offered by fellow NATO member Turkey for the US-led coalition against IS, which has taken towns in Syria right up to the Turkish border.

After four hours of talks with Erdogan on Saturday, the pair did not announce any new Turkish contribution to the coalition but Biden insisted the bilateral relationship was "as strong as ever it has been".

US officials described the talks as the latest step forward in finding common ground on Syria after Erdogan's meetings with US President Barack Obama at the NATO summit in September and with Biden himself on the sidelines of the UN General Assembly.

- 'Kobane created trust' -

A senior US official insisted that the lack of a major announcement should not be seen as a failure and the two sides had a far better mutual understanding of their respective positions than a few months ago.

"We are in complete agreement that ISIL needs to be defeated," said the official, using another name for the Islamic State. "We agree on the major objectives of the strategy."

But the official acknowledged the two sides still needed to work on their military cooperation in the crisis.

This could include use of Turkey's Incirlik airbase -- which Ankara so far has not let the United States use for bombing raids -- if Turkey's conditions were satisfied, the official said.

"Where we still need to get across the goal line is on where our military cooperation is going to be synched up," said the official.

Turkey's sole contribution so far to the military campaign has been allowing a contingent of Iraqi Kurdish peshmerga fighters to cross its territory on their way to join the fight against IS jihadists for the strategic Syrian border town of Kobane.

"Kobane became the test bed of whether we could work together," said the official. "That created more operational trust."

Turkey has repeatedly made clear that it will only increase its support for the coalition if a security zone, backed by a no-fly zone, is put in place inside Syria on the Turkish border and there is a coherent international strategy to topple President Bashar al-Assad.

The official said progress was being made between Turkey and the United States, describing exchanges as "more evolved and dynamic".

Biden, at his final press conference with Erdogan on Saturday, tellingly emphasised that they had discussed a "transition" in Syria that does not include Assad.

The warm words by Biden and Erdogan about the state of relations appeared to signal an end to a spat that erupted when the US vice president suggested in a lecture that Turkey's policy on Syria had helped trigger the rise of the IS group.

Erdogan, who is known for his quick temper and susceptibility to take offence, declared at the time that his relationship with Biden would be "history" had he said such a thing.

Turkey has also been angry that its contribution in hosting 1.6 million refugees from the Syrian conflict has gone relatively unrecognised.

Biden's office announced that the United States would provide an additional $135 million for humanitarian aid for Syria, some of which would go to refugees living in Turkey.

Before heading home after a three-leg trip that included Morocco and Ukraine, Biden met the Istanbul-based Greek Orthodox Ecumenical Patriarch Bartholomew I and visited the great Ottoman Suleymaniye Mosque.