CNN  — 

US President Donald Trump has urged Turkish President Recep Tayyip Erdogan to de-escalate the country’s military incursions in northern Syria, warning against actions that “could risk conflict between Turkish and American forces.”

The comments, which were immediately disputed by Turkish officials, represent the clearest indication yet of the seriousness in which Washington views Turkey’s military operations in northern Syria, and the potential risk they could pose to the stability of the region.

Speaking with Erdogan by phone, Trump said that Turkey’s “Operation Olive Branch,” targeting US-backed Kurdish fighters, “risks undercutting our shared goals in Syria,” according to a White House statement.

Taking a tough tone with his Turkish counterpart, Trump “urged Turkey to de-escalate, limit its military actions, and avoid civilian casualties and increases to displaced persons and refugees.”

In a sign of deteriorating relations between the two NATO allies, Turkey’s state-run Anadolu news agency reported that the official US summary “differ(ed) from the truth discussed between the Turkish and US Presidents’ phone conversation.”

A message sent to journalists from an unnamed Turkish government official also refuted US accounts.

“President Trump did not share any ‘concerns about escalating violence’ with regard to the ongoing military operation in Afrin,” read the message. “The two leaders’ discussion of Operation Olive Branch was limited to an exchange of views.”

Speaking prior to the two leaders’ conversation Tuesday, the former US ambassador to Turkey, Eric Edelman, said the currents running through Turkish domestic politics are tightly intertwined with perceptions of the US.

“The relationship between the US and Turkey has been very tense for a very long time,” Edelman told CNN. “Those tensions in some way are rooted in the nature of the regime that Erdogan is attempting to impose on Turkey, which to some degree is fueled by anti-Americanism.”

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Turkey’s ongoing air and ground strikes in the northern Syrian city of Afrin have predominately targeted Kurdish YPG fighters. The group, which is trained and armed by the US, is viewed by Ankara as a terrorist organization.

Turkey sees the quest by the Kurds – who are spread out in Turkey, Syria and Iraq – to establish an independent homeland as an existential threat to its territorial integrity and has long warned that it will not tolerate control of much of its border with Syria by the YPG.

Turkish presidential spokesman Ibrahim Kalin told CNN Tuesday that “(Turkey) had to take (military) action to protect our border.”

“This is not an operation against the Kurds of Afrin or Syria. This is an operation against a terrorist network that claims to represent the Kurds, which is far from the truth,” he said.

Turkey’s military operations, now entering into their fifth day, have involved up to 13,000 fighters, according to estimates provided by rebel groups supporting the Turkish offensive.

Ankara said it gave both Moscow and Washington advance notice of its intentions.

Syrian President Bashar al-Assad has denounced the offensive, calling it “Turkish brutal aggression on the Syrian city of Afrin,” according to the state-run Syrian Arab News Agency.

CNN’s Gul Tuysuz, Mohammed Tawfeeq, Tim Lister and Nicole Gaouette contributed reporting