A prime task of Tillerson on his trip to Ankara 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.
In response, Turkish President Recep Tayyip Erdogan threatened the U.S. with an "Ottoman slap" - a historical reference to a supposedly deadly blow.
"They have been there consistently for two or three years - nearly for the whole period that the Washington-led coalition has worked in Syria and all this time the United States special forces and other units are in Syria on the ground, illegally, without any invitation from Damascus, or without any mandate of the UN Security Council", he said.
In a hugely unusual break from protocol, the only other official present at Tillerson's meeting with Erdogan at the presidential palace was Cavusoglu who also acted as translator, United States sources said.
Tillerson arrived in Turkey on Thursday for two days of what officials have said would likely be uncomfortable discussions between the allies, which have seen their ties strained by differences over Syria.
Cavusoglu added that Turkey and the USA should fix relations and this will benefit the region. The U.S. considers them the most effective fighting force in the battle to defeat IS in Syria, and this week offered a budget plan that would send them the bulk of $550 million in new assistance.
He was referring to the ongoing operation by Turkish military in Afrin, Syria in a bid to oust the Kurdish militia of the Kurdish People's Protection Units (YPG). We're going to lock arms.
Ties were damaged after the failed coup of 2016 with Turkey stung by a perceived lack of USA solidarity and angered by Washington's refusal to extradite Fethullah Gulen, a Pennsylvania-based cleric accused of ordering the putsch.
And he further upped the ante by warning U.S. troops to leave Manbij, a YPG-held town east of Afrin, raising fears of a clash between the allies.
He even warned that the United States risked being dealt an "Ottoman slap" in Syria - a backhand thwack which, according to legend, could kill an opponent at a stroke.
But the Turkish government views the Kurdish fighters as an "extension of the outlawed Kurdistan Workers' Party (PKK), which has fought a decades-long war against Ankara", says Al-Jazeera.
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.
"Our relations were at a critical turning point", Cavusoglu said.
It was unclear whether Tillerson's visit could achieve any kind of breakthrough.
Canikli said he told Mattis that USA support for such militants has enabled Kurdish rebels in Turkey "to grow and strengthen", posing an increasingly "existential" danger to Turkey.
"With the will that we put forward as of yesterday, we have taken an important turn in terms of normalizing our relations".
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