Moscow's warning came shortly before Russian and Syrian security forces were due to start overseeing the removal of YPG fighters and weapons at least 30 kilometres into Syria, under the deal struck by Russian and Turkish presidents Vladimir Putin and Recep Tayyip Erdogan.
"The vice president welcomes this development and sees it as having satisfied the terms of the 17 October agreement, as pertains to the withdrawal of the YPG", Waldman said, using the initials of the Kurdish People's Protection Units, which formed the backbone of the SDF but which Turkey considers a terror group.
A ceasefire for Kurdish fighters has been extended for another six days.
Mazloum Kobani, commander of the mostly Kurdish Syrian Democratic Forces, informed US officials that his troops had completed the withdrawal a couple of hours before the end of the cease-fire.
The Turkish campaign displaced almost 180,000 people and prompted the SDF to strike a bargain with the government of Syrian President Bashar al-Assad, allowing for the return of some pro-Assad forces to areas once under Kurdish control.
The Russia-Turkey deal goes a considerable way to restoring the control of Moscow's ally, the Syrian government, across much of the northeast.
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United States troops had been in the region supporting Kurdish fighters who had been allies combating the ISIS in the area, but were pulled out by Donald Trump.
In a further sign of growing ties between Ankara and Moscow, which have alarmed Washington, the head of Russia's defense sales agency was quoted by Interfax news agency as saying Moscow could deliver more S-400 missile defense systems to Turkey.
Russian Federation has powerful sway on all sides.
The area in question is a 120km-long strip between the towns of Ras al-Ain to Tal Abyad, where the Turkish operation is taking place. Turkey received guarantees from Russian Federation and Damascus that Kurdish forces will be removed from its border.
Ankara had threatened to relaunch its offensive but said late in the evening that "at this stage, there is no further need to conduct a new operation outside the present operation area".
No comment on the deal from the SDF or Kurdish political leaders was immediately forthcoming.
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President Trump will make an announcement on Wednesday about the implementation of a safe zone in northern Syria, where Turkish fighters had led an offensive against Kurdish forces.
"Nothing about this makes sense from a U.S. national security perspective", the senior official said. "I hope that this agreement is beneficial to our countries and to our brothers in Syria", Erdogan said.
Prior to the Sochi meeting, Erdogan emphasized that "Turkey does not have an eye on any country's territory" - calling such an accusation an "insut".
Since then the ceasefire has largely held, despite what U.S. officials have described as "some minor skirmishes". Idlib and the northeast safe zone can become quid pro quo in future Russia-Turkey talks.
US forces have withdrawn from several bases in Syria, including from the key town of Manbij and another close to Kobane close to the Turkish border.
Kobani is of special significance to the Kurdish fighters, who fought off Islamic State militants trying to seize the city in 2014-15 in one of the fiercest battles of Syria's civil war. Defense Secretary Mark Esper insisted Monday that the United States "had no obligation" to defend the Kurds from Turkish attack.
Some EU states argue for freezing funds, others want EU money to continue flowing to Turkey to keep most refugees there and avoid a repeat of a 2015 crisis in which hundreds of thousands of war refugees poured into Europe from Turkey.
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Mr Jeffrey said he was not consulted about Trump's plan to withdraw troops.