This strategy aims to prevent Islamic State militants from returning to areas recently conquered from them, U.S. officials say. But Tillerson articulated a number of other goals for the new policy, including rolling back Iranian influence, defeating al-Qaeda and securing a peaceful settlement of the Syrian conflict that excludes President Bashar al-Assad.
Washington's focus on providing military support to Syrian Kurds battling the Islamic State, however, has always been rife with contradictions, experts say. These are now coming to the fore as longtime U.S. ally and fellow NATO member Turkey takes on the United States' biggest Syrian ally in the fight against the Islamic State.
"This highlights the fundamental difficulty of a U.S. strategy that requires maintaining active alliances with two forces which are at war with each other," said Noah Bonsey, a Syria analyst at the International Crisis Group who is on a visit to the Kurdish areas of northeastern Syria. "There has never been an easy answer to that, and there isn't going to be one."
Since the assault began a week ago, Washington has scrambled to strike a balance between its warring friends, acknowledging the validity of Turkey's security concerns while urging Ankara to restrict the scope of the offensive to the border region of Afrin and to limit casualties.
Turkey has been waging a decades-old war at home against Kurdish insurgents of the Kurdistan Workers' Party, or PKK, which is allied to the U.S.-backed group controlling territory along the Turkish border in northern Syria. The PKK is designated a terrorist group by Washington and Ankara.
The U.S. military has meanwhile made clear it will not go to the aid of the Kurds in Afrin because it does not regard them as allies on par with the Kurds farther east who were trained and armed to fight the Islamic State. The Kurds in Afrin were not involved in fighting the Islamic State and have not received American assistance, U.S. officials say.
But with Turkish President Recep Tayyip Erdogan intensifying his threats to extend the Turkish offensive to the areas farther east, where the U.S. military maintains troops, a larger conflict looms.
On Saturday, he issued an ultimatum to U.S. troops to withdraw from Manbij, which has been controlled by the U.S.-backed, Kurdish-led alliance since it was captured from the Islamic State in 2016. Manbij in turn borders a part of northern Syria controlled by other Syrian rebels backed by Turkey. U.S. troops have been conducting patrols in the area for nearly a year to keep their hostile allies apart.
A Turkish attack on Manbij would present the United States with a major dilemma, said Gonul Tol, director of the Center for Turkish Studies at the Middle East Institute in Washington.
If the Trump administration intends to remain in northern Syria, "they need the Kurds," she said. "On the other hand, Turkey is a NATO ally. They might be forced to pick a side."
In the past, U.S. officials have privately dismissed Erdogan's frequent threats to attack Manbij as rhetoric intended primarily for domestic consumption in Turkey. But domestic politics means such an attack could become inevitable, Tol said.
"Erdogan talked about this so much, it's going to be difficult for him to walk it back," she said. Erdogan's primary focus has been a presidential election in Turkey scheduled for next year, and the intensifying confrontation with Washington works in his favor politically at home, she said.
Meanwhile, other regional players in Syria are hardly more enthusiastic than Turkey about the prospect of a long-term U.S. troop presence in Syria or about the existence of the Kurdish autonomous zone the troops appear to be cementing. Russia has given the nod to the Turkish offensive, which is unfolding in an area demarcated as under Russia's overall influence, U.S. officials say.
"Turkey and Russia struck an agreement to allow the Turkish offensive to take place," a senior U.S. administration official said at a briefing for journalists last week in Washington. The Russians essentially "greenlighted" the operation, said the official, who spoke on the condition of anonymity to discuss the sensitive subject.
The bigger problem, said Faysal Itani, a resident senior fellow at the Atlantic Council, is the U.S. presence in Syria is so small and the hostility to the U.S. troops so widespread that it is hard to see how they can influence events. The United States maintains 2,000 troops in an area the size of Indiana, alongside the Kurdish-Arab alliance known as the Syrian Democratic Forces. The dominant group in the alliance is the Kurdish People's Protection Units, or YPG, which has close ties to the PKK.
Syria and Iran also are unhappy about American plans to remain in Syria, and the Turkish offensive appears only to have brought Turkey, Russia, Iran and Syria closer together, analysts say.
"Keeping 2,000 troops on the desert margins of Syria in alliance with a group the entire region hates is not really leverage," Itani said. "It does, however, get others to unite against us. The Turkish incursion into Afrin shows just how few friends we have in Syria."
Turkey's wrath was initially sparked by reports from northeastern Syria that the United States was training a 30,000-member force to patrol the borders of the autonomous Kurdish enclave that has emerged from Syria's seven-year-old war. U.S. officials have since backtracked, saying they never intended the force to be deployed along the border with Turkey but to guard against infiltration by the Islamic State from Iraq and other parts of Syria.
Turkish anger with U.S. policy is not new; it dates to the Obama administration's decision to arm the Syrian Kurds to fight the Islamic State in 2015, said Robert Ford, a former U.S. ambassador to Syria who is now a senior fellow at the Middle East Institute and teaches at Yale University.
"Back in 2011, Turkish officials stressed to me that their nightmare scenario was a break-away Syrian Kurdish region in northeast Syria. The Turks' nightmare has arrived, with huge, conscious help from the Americans," Ford wrote in an email. "Whatever the name of the security force the Americans are helping construct in eastern Syria, the Turks will view it as helping anchor that Syrian Kurdish breakaway region, and there will be conflict."
The United States has viewed Syria through the narrow prism of defeating the Islamic State since 2014, and with the extremists on the brink of defeat, Washington finds itself with no alternative vision, said Sam Heller, a fellow at the Century Foundation, in comments made from Beirut.
"What the Turks are doing here is keying into the illogic of the American campaign" against the Islamic State, he said.
U.S. officials dispute widespread characterizations of their plans for a continuing troop presence in Syria as indefinite, pointing out that their strategy articulates clear goals.
But those are ambitious and almost certainly elusive objectives that are unlikely to be realized anytime soon, Itani said. "The goals are too ambitious for what we're willing to do, regardless of whether Turkey controls Afrin," he said. "On top of that, every major actor in Syria is now working against us in one way or another."
Sly reported from Beirut and Fahim from Istanbul. Missy Ryan and Greg Jaffe in Washington and Zakaria Zakaria in Istanbul contributed to this report.