Tillerson also emphasized Washington's concerns regarding the detentions of US employees in Turkey and called for the release of American Pastor Andrew Brunson.
Turkey has suggested joint operations with the U.S. in the past as an alternative to the USA alliance with the Kurds.
Turkey launched an air and ground offensive last month on the Afrin region, opening a new front in the multi-sided Syrian war, to target Kurdish fighters in northern Syria.
The PKK is blacklisted as a terror group by the U.S. and EU. Ankara considers the YPG to be an arm of the PKK, a banned group that has waged a decades-long insurgency in Turkey.
A prime task of President Donald Trump's top diplomat is to allay Turkish anger over U.S. policy in Syria, a dispute which has ignited the biggest crisis in bilateral ties since the 2003 Iraq war.
Turkey had threatened to attack US-allied Kurdish forces in Manbij, regarding them as terrorists, the BBC reports. While the Kurds have provided the bulk of the ground troops for the US -led coalition battling the Islamic State militant group, Turkey considers them violent separatists and a threat to its national security.
But speaking in Beirut before his meeting with Erdogan, Tillerson denied ever giving heavy weaponry to the YPG. "We were either going to correct this or it was going to take a turn for the worse".
While Tillerson was meeting his Turkish counterpart, Mevlut Cavusoglu, a crowd outside the venue chanted, "Murdering Americans", in a stark illustration of how low bilateral relations have sunk.
Tillerson also promised that weapons provided by the U.S.to the YGP-led Syrian Democratic Forces (SDF) would be limited and "aimed only at military objectives".
On a note of discord, the foreign minister said the USA had dishonoured a previous pledge to make sure Kurdish forces pulled back east across the Euphrates river.
A State Department spokesperson refused to confirm whether Tillerson declined to use an American translator, or if so, why.
Turkish President Recep Tayyip Erdogan has repeatedly said that Afrin should be cleared of "terrorists", and demanded the deployment of Turkish troops there during a speech back in November 2016.
Tillerson acknowledged how close the North Atlantic Treaty Organisation allies had come to a breakdown in relations. "I hope this will happen very soon". Russian Federation and Iran, allied with Syria's Assad regime, have been making deep inroads in Syria.
"Negotiations points are restricted between Ankara and Washington", remarked Demirtas.
Tillerson's visit is part of a flurry of high-level meetings between top US and Turkish officials in recent days. The U.S. has been supporting the YPG in order to fight IS in northern Syria.
Top French officials have warned Ankara against "adding war to war" in Syria, and Germany suspended decisions on new weapon supplies to Turkey.
"Our relations were at a critical turning point", Cavusoglu said.
The United States in turn is unhappy that Turkey has arrested thousands of its own citizens, as well as Americans and Turkish employees of the U.S. Embassy and consulates who U.S. officials say were just doing their jobs.
Kurdish fighters from the People's Protection Units head a convoy of U.S military vehicles in the town of Darbasiya next to the Turkish border.
The pilot told the man to cease breaking wind, but the passenger either was unable to hold back or simply refused to do so. Taking note of the situation, pilots made a decision to land in Vienna , reporting "passengers on the rampage".
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While Trump lawyer Michael Cohen confirms he "facilitated" the payment to Daniels, he has not disclosed its goal . After Trump won the presidency, however, A.M.I.'s promises largely went unfulfilled, according to McDougal.
The man they called "Drey" allegedly told the girls they could earn $2,000 doing some modeling and by performing in music videos. Airline worker Denice Miracle became concerned when teens aged 15 and 17 approached the ticket counter on August 31 a year ago .
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