Perhaps with a view to that potential flash point in western Syria, and another one farther east around the city of Manbij, Mr. Tillerson vowed after the meeting that the days when the two countries operated independently in the fight against the Islamic State were over.
“We’re not going to act alone any longer. We’re not going to be the U.S. doing one thing and Turkey doing another,” Mr. Tillerson said. “We’re going to act together from this point forward. We’re going to lock arms. We’re going to work through the issues that are causing difficulties and we’re going to resolve them and we’re going to move forward.”
But while the war in Syria is perhaps the most pressing of the disagreements between the two countries, it is by no means the only one.
The Trump administration has also been perturbed by Mr. Erdogan’s creeping authoritarianism, his increasingly cozy relations with Moscow, his security detail’s brazen attack in Washington on peaceful protesters, and Turkey’s arrests of American citizens and State Department employees.
The Turks, for their part, are furious at the administration’s refusal to extradite the Muslim cleric Fethullah Gulen, whom Turkey accuses of orchestrating a 2016 coup from his self-imposed exile in Pennsylvania.
The last time Mr. Tillerson was in Ankara, he showered praise on the Turks and largely avoided listing American grievances, while receiving an earful of complaints. This time, he was much tougher in his remarks, reflecting his growing belief in the importance of the public aspects of diplomacy.
“We continue to have serious concerns about the detention of local employees of our mission in Turkey and about cases against U.S. citizens who have been arrested under the state of emergency,” he said. He called for the release of Andrew Brunson and Serkan Golge, American citizens caught up in Mr. Erdogan’s post-coup purge.
Mr. Tillerson’s trip here is part of a flurry of high-level meetings between top American and Turkish officials in recent days. In Brussels on Thursday, Defense Secretary Jim Mattis met with his Turkish counterpart, while the national security adviser, Lt. Gen. H. R. McMaster, met on Sunday in Istanbul with Turkey’s senior presidential adviser, Ibrahim Kalin.
The seeds of the rift between the two countries were planted in 2014, as the Islamic State swept across Iraq and Syria. Looking for partners, President Barack Obama pleaded with Mr. Erdogan to help in the fight against the militants, but Mr. Erdogan initially refused.
With the Iraqi Army in shambles, the Americans reached out to the Kurdish militias, the only force in the region not aligned with Iran that was able and eager to fight. The Americans knew that their use of Kurdish forces might one day lead to a reckoning with Baghdad and Ankara, but felt they had little choice.
In Iraq, that day came in October, when the Iraqi army attacked the oil-rich and ethnically divided city of Kirkuk, driving Kurdish forces out. In Syria, the reckoning has only just started.
American officials have tried to mollify the Turks by insisting that their support of the Kurds is limited in time and resources. But news that Washington was preparing to fashion a 30,000-strong Syrian border force out of the Kurdish-led Syrian Democratic Forces, or Y.P.G. — a plan since disavowed by the Trump administration — was the “last straw,” Fahrettin Altun, a columnist for a pro-government newspaper, Daily Sabah, wrote Thursday. That announcement directly precipitated Turkey’s military offensive against Kurdish militias in the enclave of Afrin in western Syria, Mr. Altun wrote.
Turkey views the Y.P.G. as an arm of the Kurdistan Workers’ Party, or P.K.K., an insurgent group in Turkey that has carried out attacks here for decades. The Turkish view of the connection between the two groups was bolstered this week by an American intelligence assessment equating them and concluding they “probably will seek some form of autonomy” — exactly what Turkey fears.
The last time Mr. Tillerson was in Ankara, the Turkish news media was in a frenzy about a leaked phone record that to them suggested American collusion in the 2016 coup, an accusation American officials found almost laughable. This time, newspapers were filled with references to the “Ottoman slap.” Public expressions of anti-American sentiment here have become routine and intense since the coup in 2016.
In an indication of just how far apart the two sides remain, Mr. Cavusoglu said that Mr. Tillerson had promised that the Y.P.G. would soon leave the strategically important city of Manbij.
“Once the Y.P.G. leaves there, we will have trust,” Mr. Cavusoglu said. “This is a commitment that the United States of America has made to us and we will be talking about how this implementation will be made.”
In his own remarks, Mr. Tillerson would say only that security around Manbij was “a topic of discussion going forward.”
The Turkish military has been advancing slowly in its offensive against Kurdish militias in Afrin. So far it has cleared 44 villages, the Anadolu news agency reported, but has yet to take any of the main towns. Turkey has lost 31 soldiers in the operation that began on Jan. 20, the Defense Ministry says.
Turkish officials say the Kurdish militias in Afrin have fired more than 100 rockets and mortars over the border into Turkey in that time, killing seven civilians and one soldier in a border observation post.