This tentative warming of relations, however, is already coming at a cost to the US. Saying they feel let down by Washington, US-allied Kurdish forces said last week they are withdrawing from the front lines of the fight against the Islamic State in southern Syria to join the battle against Turkey in the north.

The US, which has pursued Islamic State forces with single-minded focus, has long insisted the Kurds were the most effective partners in the fight against the militants, despite Turkish complaints.

US commanders on the ground in and around Manbij have previously warned that several hundred American troops deployed there would defend the Kurds against any attack by Turkish troops, now massed a few kilometres away. Turkish officials were outraged last month when US commanders touring the area with American journalists praised the Kurds and vowed to fight alongside them if there were a Turkish attack.

A shootout between two NATO members, both agree, would be catastrophic.

The US relationship with Turkey has been on a downward trajectory for several years because of what both sides have been doing, and seeking, during Syria's civil war. An outright rift between the countries has seemed increasingly likely in recent months.

Beyond quarreling over the Kurds, the US and Turkey have also traded diplomatic volleys in the aftermath of a coup attempt in Turkey in 2016. Turkish President Recep Tayyip Erdogan has stoked anti-American sentiment at home, and American policymakers have explored the possibility of imposing sanctions on Turkey in response to Erdogan's increasingly authoritarian policies.

The possibility of a deal over Manbij has, at least temporarily, cooled temperatures, according to senior US and Turkish officials who spoke on the condition of anonymity about the still-tenuous rapprochement. The meetings that began last week, which are set to continue in both capitals over the coming months, will deal with a constellation of divisive issues, another senior Turkish official said, including the Trump administration's opposition to Turkish plans to buy a Russian surface-to-air missile system.

The Turkish official said "the Americans understand our concerns more clearly" after visits last month to Turkey by US Secretary of State Rex Tillerson and Trump national security adviser HR McMaster. Defence Secretary Jim Mattis also met with his Turkish counterpart in Europe.

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Other issues dividing Washington and Ankara have also proved daunting, including Turkey's repeated insistence that the United States extradite Fethullah Gulen, a Pennsylvania-based Turkish cleric whom Erdogan accuses of directing the failed coup. US officials have chafed at this pressure to extradite Gulen.

US lawmakers, meantime, have become increasingly impatient with Erdogan's broad crackdown on dissidents, journalists and others after the coup attempt, and with the Turkish imprisonment of US citizens. A brawl in May outside the Turkish ambassador's residence in the District of Columbia, where police said Erdogan's personal guards attacked anti-Erdogan protesters, also prompted outrage.

Several US lawmakers have called on the Trump administration to impose sanctions against the Turkish government. Some  have said that the upcoming State Department spending bill should require the secretary of state to block entry of Turkish officials who are "knowingly responsible for the wrongful or unlawful prolonged detention of citizens or nationals of the United States".

Washington Post