Secretary of State Rex Tillerson met for more than two hours on Thursday with Turkey's president, Recep Tayyip Erdogan, as they hoped to shore up troubled relations between their nations. Making his first trip to Turkey, Tillerson became the highest-ranking Trump administration official to hold a face-to-face session with Erdogan, an increasingly authoritarian leader who is also a NATO member and key ally in the fight against Islamic State in Syria. From Our Partners: Snap to Lose $2 Billion This Year The meeting went longer than planned. Turkey and the United States disagree sharply on how to combat Islamic State: Washington supports Kurdish militias that Erdogan regards as an arm of the Kurdistan Workers' Party (PKK), which Turkey and the U.S. consider a terrorist organization. "Trying to fight against Daesh through terrorist organizations such as ... extensions of the PKK, would be like shooting yourself in the foot," Erdogan's senior advisor, Ibrahim Kalin, said ahead of Thursday's meeting. Daesh is a pejorative Arabic acronym for Islamic State. Turkey's role is especially crucial as a battle looms to recapture the Syrian city of Raqqah, occupied by Islamic State and declared its capital. Turkey sent hundreds of troops and heavy armor into Syria last summer to back thousands of rebels with the Free Syrian Army, another militia that has carved out a swath of land along the Syrian border and is now poised to expand into two Kurdish enclaves. American troops aiding the Kurds are in those same enclaves, which sit between Turkish forces and Raqqah. Turkey has said it could provide boots on the ground in an offensive on Raqqah — if the Kurdish forces are sidelined. But Tillerson did not appear willing to withdraw U.S. support for the Kurdish militias, which have often proved to provide the most effective fighters on the battlefield. The relationship between Turkey and the United States is fraught with tension. During President Trump’s election campaign, Erdogan joined a number of world leaders in blasting the candidate's insults toward Muslims and his call to ban Muslims from entering the US. Erdogan, who has championed himself as a leader in the Muslim world, has long blamed Western biases toward Islam for Turkey’s inability to become a member of the European Union. Last July, Erdogan called for Trump’s name to be removed from an Istanbul development project. But by the time Trump was inaugurated, Erdogan’s tone had changed, and Turkish leaders — who had become disenchanted with the Obama administration — were expressing expectations for a more malleable relationship with Trump. Prime Minister Binali Yildirim, in a congratulatory message to Trump, said he hoped the new president would take steps to extradite Fethullah Gulen, an Islamic cleric living in Pennsylvania whom Turkey blames for a deadly, failed coup on July 15. Turkey’s repeated calls for Gulen’s extradition have gone largely unheeded in Washington, as the Justice Department, under both President Obama and now Trump, has insisted that thousands of pages of evidence Ankara provided on Gulen be examined by a judge before any decision is made. Gulen has denied any role in the coup attempt. Part of the reason for Turkey’s optimism on Trump stemmed from its relationship with Trump’s former national security advisor, Michael Flynn, who resigned in February over undisclosed contacts with Russian officials. Flynn has since disclosed that he was also paid $500,000 by a Turkish businessman to lobby on behalf of Ankara, and that he met with senior Turkish officials to discuss "whisking" Gulen out of the U.S., sidestepping formal extradition. Tillerson also met with Yildirim on Thursday. The two "discussed working to enhance our critical security and economic ties in the region," a U.S. official said. Later Thursday, Tillerson was scheduled to travel to Brussels, where he will attend a daylong conference with the full roster of NATO allies.