US Secretary of State Rex Tillerson faces "difficult" talks next week with Nato ally Turkey on Syria and human rights, his delegation said before a regional tour.
Late last month, Ankara began a cross-border offensive in north-western Syria against a Kurdish militia it deems to be a terrorist group. Washington supports and arms the militia — known as the People's Protection Units (YPG) — which has been its main ally in the battle against ISIL.
The Turkish operation has further raised tensions between Turkey and the United States, whose relations were already complicated.
"We are urging them to show restraint in their operations in Afrin, and to show restraint further along the line across the border in northern Syria," a senior US State Department official told reporters on Friday, two days before the start of Mr Tillerson's five-nation tour.
"You start with asking for restraint and look for ways that you can help bring it to an end as quickly as possible."
The official's comments came just hours before Turkey said one of its military helicopters had been "downed" during the offensive in Afrin, Associated Press reported.
The Turkish military said two soldiers were killed in the incident, which occurred at around 1pm local time on Saturday.
Announcing the incident in Istanbul, President Recep Tayyip Erdogan did not mention by name the YPG, but said those responsible for the downing would pay for it. The YPG meanwhile claimed responsibility, saying the chopper had been downed in Raju, north-west Afrin.
As the three-week-old offensive continues, Mr Erdogan has called on the US to pull its troops back from Syria's Manbij, which is east of Afrin.
"Obviously we need to work with the Turks to figure out more about what their long-term intentions are," and to try to find a way "to address their legitimate security concerns while, at the same time, minimising civilian casualties and above all else keeping everything focused on the defeat-ISIS fight, which is not over," the official said.
It will be "a difficult conversation", the official continued, referring to the "very hot" Turkish rhetoric on the subject.
Mr Tillerson's visit is also expected to touch on other sensitive topics.
These include human rights and arrests that the US called "arbitrary" following a state of emergency declared after an attempted coup in 2016.
Turkey last year detained local employees of American diplomatic missions in the country, and arrested Taner Kilic, the president of Amnesty International in Turkey.
"There's no pulling punches on that," a second senior State Department official said.
"We've been very public in our call to the Turks to let these folks go, and we've been very firm in our private conversations with them as well."
He conceded: "The Turks are angry and this is a difficult time to do business."
But Washington believes the two countries share fundamental underlying interests including Syria's stability, the defeat of ISIL, and countering the Kurdistan Workers' Party (PKK) which both Ankara and the West consider terrorists.
Mr Tillerson's Middle East tour will also take him to Cairo, Kuwait City, Amman and Beirut.
