Russian military police have begun patrols on part of the Syrian border.
The move came as they quickly implemented an accord with Turkey that divides control of north-eastern Syria.
The Kremlin told Kurdish fighters to pull back from the entire frontier or else they would face being “steamrolled” by Turkish forces.
Turkish President Recep Tayyip Erdogan echoed those warnings, saying his military would resume its offensive against Kurdish fighters if the new arrangements are not carried out.
Mr Erdogan and Russian President Vladimir Putin reached an agreement on Tuesday that would transform the map of north-east Syria, installing their forces along the border and filling the void left by the abrupt withdrawal of American troops.
The Kurdish fighters, who once relied on the US forces as protection from Turkey, were given a deadline of next Tuesday evening to pull back from border areas they have not already left.
Iraq, meanwhile, closed the door on the US military’s attempt to keep the troops leaving Syria on its soil.
Iraqi defence minister Najah al-Shammari said that those troops were only “transiting” Iraq and would leave within four weeks, heading either to Kuwait, Qatar or the United States.
Mr al-Shammari spoke after meeting US defence secretary Mark Esper, who earlier this week had said the American forces from Syria would remain in Iraq to fight the so-called Islamic State group. Iraqi’s military said they did not have permission to do so.
The clumsy reversal underscored the blow to US influence on the ground in the wake of President Donald Trump’s order for US troops to leave Syria.
Those forces were allied to the Kurdish-led fighters for five years in the long and bloody campaign that brought down the Islamic State group in Syria.
Now a significant swathe of the territory they captured is being handed over to US rivals, and the Kurds have been stung at being abandoned by their allies to face the Turkish invasion launched on October 9.
The Kremlin pointedly referred to that abandonment as it told the Kurds to abide by the Russian-Turkish accord.
“The United States was the closest ally of the Kurds during the last few years, and in the end the US ditched the Kurds and effectively betrayed them,” said Kremlin spokesman Dmitry Peskov, according to Russian newswires.
“It’s quite obvious that if the Kurdish units don’t withdraw with their weapons then Syrian border guards and Russian military police will have to step back. And the remaining Kurdish units will be steamrolled by the Turkish army,” he said.
Turkey considers the Kurdish fighters terrorists because of their links to Kurdish insurgents in Turkey. It has demanded they retreat from the entire border region, creating a “safe zone” where Turkey could also settle some of the 3.6 million Syrian refugees on its soil.
Ankara would gain that goal under the new accord with Moscow along with the agreement last week with the US that put a ceasefire in place.
Kurdish forces completed withdrawing on Tuesday from a stretch of territory 75 miles wide along the border and 19 miles deep between the towns of Ras al-Ayn and Tal Abyad. That pullback, allowing Turkish-backed forces to take over, was required under the US-Turkish accord.
The new agreement with Russia allows Turkey to keep sole control over that area. For the rest of the north-eastern border, Russian and Syrian government forces will move in to ensure the Kurdish fighters leave.
Then after the deadline runs out on Tuesday, Turkish and Russian forces will jointly patrol a strip six miles deep along the border.
The Russian defence ministry said a convoy of military police had crossed the Euphrates River and deployed in the Syrian border town of Kobane.
“The military police will help protect the population, maintain order, patrol the designated areas and assist in the withdrawal of Kurdish units and their weapons 30 kilometres away from the border,” it said.
The Turkish military said it would not resume its offensive “at this stage” after the US-brokered ceasefire expired on Tuesday night.
However, foreign minister Mevlut Cavusolgu said that Turkish forces would “neutralise” any Syrian Kurdish fighters they come across in areas that Turkey now controls.
President Erdogan said the attack would start again if the Kurdish pullback does not take place.