Rex Tillerson held talks Tayyip Erdogan in Ankara to ease Turkish anger over US policy in Syria.

ANKARA (AFP) - US Secretary of State Rex Tillerson on Thursday held talks with Turkish President Recep Tayyip Erdogan in Ankara, seeking to ease tensions between the NATO allies that reached new heights over Ankara s ongoing operation inside Syria.

A prime task of President Donald Trump s top diplomat is to allay Turkish anger over US policy in Syria, a dispute which has ignited the biggest crisis in bilateral ties since the 2003 Iraq war.

But Turkish presidential sources said Erdogan made no secret of Turkey s concerns during the over three-hour meeting with the former chief of energy giant Exxon Mobil.

"In the talks, Turkey s priorities and expectations on all these topics were clearly conveyed to the US secretary of state," said a source, asking not to be named.

Tillerson will meet on Friday morning Foreign Minister Mevlut Cavusoglu who was the only other official present at the meeting and acted as translator, US sources said.

A State Department official said Tillerson and Erdogan had a "productive and open" conversation about a "mutually beneficial way forward" for US-Turkey ties.

Turkey s operation against the People s Protection Units (YPG) Kurdish militia in the Afrin region of Syria has added a potentially insurmountable new problem to an increasingly rough bilateral relationship.

Analysts said the level of tension was similar to 2003 when Turkey refused to let US troops operate from its territory for the Iraq war, or even the aftermath of Ankara s invasion of Cyprus in 1974.

Turkey s operation against the YPG, which Ankara blacklists as a terror group, has seen Turkish troops fighting a militia which is closely allied with the US in the battle against Islamic State (IS) group jihadists.

Speaking in Beirut before his meeting with Erdogan, Tillerson denied Washington ever gave heavy weaponry to the YPG and thus could not gather up such arms, as desired by Ankara.

"We have never given heavy arms to the YPG so there is none to take back," Tillerson said.

Erdogan earlier this month accused Washington of sending in thousands of truckloads and planeloads of weapons to the YPG in Syria, asking why the US still had a presence there if the jihadists had been defeated.

And he further upped the ante by warning US troops to leave Manbij, a YPG-held town east of Afrin, raising fears of a clash between the allies.

He also warned that the US risked being dealt an "Ottoman slap" in Syria -- a backhand thwack which, according to legend, could kill an opponent at a stroke.

For Ankara, the YPG is a branch of the outlawed Kurdistan Workers  Party (PKK), which is blacklisted as a terror outfit by the US and the EU.

But for Washington, the YPG is an ally against IS jihadists and Turkey s operation is a distraction from efforts to ensure the extremists are permanently defeated.

But Cavusoglu this week warned Washington that ties were at a "critical point" at which relations would "be fixed or... completely damaged."

It was unclear whether Tillerson s visit could achieve any kind of breakthrough.

Following a meeting with US Defense Secretary Jim Mattis in Brussels, Turkish Defence Minister Nurettin Canikli said Ankara wanted to see the YPG pulled out of the Syrian Democratic Forces (SDF) umbrella group.

He said Mattis had promised greater support in Turkey s fight against the PKK in their rear bases in northern Iraq.

The squabble over Syria is, however, just one of a litany of issues burdening Turkey-US relations.

Ties were damaged after the failed coup of 2016 with Turkey stung by a perceived lack of US solidarity and angered by Washington s refusal to extradite Fethullah Gulen, a Pennsylvania-based cleric blamed for ordering the putsch.

And Washington has expressed concern that several of its citizens -- as well as at least two Turkish employees of US missions -- have been caught up in the post-coup crackdown.

Last week, NASA scientist Serkan Golge, a dual national, was jailed for seven-and-a-half years for being a member of Gulen s movement, while US pastor Andrew Brunson, who ran a church in Izmir, who has been held on similar charges since October 2016.

Turkey also has a key lever in its hosting of US airbase at its southern military airport of Incirlik close to Syria, which houses dozens of American tactical nuclear weapons and which the conservative Turkish press has repeatedly said should be shut.