The US secretary of state has started a two-day visit to Turkey, where Rex Tillerson hopes to ease increasing tension between US and Turkish officials over the conflict in Syria.

A war of words between the NATO allies has escalated ever since Turkey launched a military offensive into the Afrin region of northern Syria last month in an effort to root out Kurdish YPG fighters, who figure among a US-backed coalition of armed groups.

On the heels of visits to Kuwait, Jordan and Lebanon, Tillerson arrived in the Turkish capital, Ankara, on Thursday where he met President Recep Tayyip Erdogan.

Earlier this week, Turkey demanded the US expel the YPG from the Syrian Democratic Forces (SDF) coalition, which has been fighting Islamic State of Iraq and the Levant (ISIL, also known as ISIS) in Syria with support from the US.

"We demanded this relationship be ended," Nurettin Canikli, Turkey's defence minister, told reporters in a briefing in Brussels on Thursday.

The Turkish government views the YPG as an extension of the outlawed the Kurdistan Workers' Party (PKK), which has fought a decades-long war against Ankara.

"We want them [the US] to end all the support given to the Syrian arm of PKK, the YPG," Canikli said, as reported by Reuters news agency.

War of words

Earlier this month, Erdogan accused the US of sending stockpiles of weapons to the YPG in Syria, a claim Tillerson himself denied on Thursday.

The US has "never given heavy arms" to the YPG and, therefore, there is "nothing to take back", Tillerson said.

Turkey has also demanded that US troops leave Manjib, a Syrian town east of Afrin that is held by the Kurdish militia, or risk a confrontation.

In response, Paul Funk, the commander of US forces in Syria and Iraq, said the US and its partners in Syria would hit back if attacked.

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"You hit us, we will respond aggressively. We will defend ourselves," Funk said, during a visit to Manjib this month.

The Turkish president then threatened to deliver an "Ottoman slap" - a tactic used by Ottoman forces in the 17th century that, according to legend, could be instantly fatal - if the US does not get out of the way.

While Tillerson has taken a conciliatory tone saying this week the US was "keenly aware of the legitimate security concerns of Turkey", officials in Ankara have been more blunt.

"Our ties have reached a very critical stage," Mevlut Cavusoglu, Turkey's foreign minister, said on February 12, local media reported.

"Either we improve our ties, or they will deteriorate completely."

Other issues

The increasingly complex political reality in Syria has led to what Staffan de Mistura, the UN special envoy to Syria, described as the most "violent, dangerous and worrying" situation he has witnessed since he took up his post four years ago.

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"What we are seeing in Syria today not only imperils the de-escalation arrangements and regional stability, it also undermines the efforts for a political solution," de Mistura said on Wednesday.

But Syria is not the only cause of strained ties between Washington and Ankara.

Last year, the two countries temporarily suspended non-immigrant visa services at their respective embassies over the arrest of several staff members at the US consulate in Istanbul.

Turkish officials alleged the staff members had ties to Muslim leader Fethullah Gulen, whom Ankara accuses of being responsible for a deadly failed coup in 2016.

While Gulen, who lives in self-imposed exile in the US, has denied the allegations, the Turkish government has put pressure on Washington to extradite Gulen to face charges for the attempted putsch.

The United States has so far refused to extradite the Muslim leader.