Units have already entered the two key border towns of Kobane and Manbij.

Under the deal agreed by Russia and Turkey, Kurdish fighters were given 150 hours from noon on Wednesday to pull back 30km (18 miles) along the border.

Turkish troops will continue to control an area they took during a recent offensive against the Kurdish fighters, regarded by Turkey as terrorists.

Part of Turkey's plan is also to create a "safe zone" along the border that will house some two million of the Syrian refugees it hosts.

The Turkish offensive began after the US announced a sudden and unexpected withdrawal of its troops from northern Syria. The US troops had been supporting the Kurdish fighters, who have been allies in the fight against the Islamic State (IS) group in the region.

US President Donald Trump tweeted on Wednesday that the situation in the border area had been a "big success", and said he would speak in detail later.

The deal was negotiated by Turkish President Recep Tayyip Erdogan and Russia's Vladimir Putin after lengthy talks in the Black Sea resort of Sochi on Tuesday.

It was agreed that Russian and Syrian forces would oversee the Kurdish pullback in an area from the Euphrates river, just east of Manbij right up to the Iraqi border in the east.

On Wednesday, Russia's defence ministry said its forces had crossed the river at noon (09:00 GMT) and "advanced towards the Syrian-Turkish border".

Convoys of military police were later seen arriving in Kobane and Manbij, some 60km apart.

Both towns lie outside the area forming part of Turkey's military operation, and Russia's foreign ministry said on Wednesday Turkish forces would not be deployed there, according to Ria Novosti news agency.

The deal does not cover the area currently under Turkish military control - between the towns of Ras al-Ain and Tal Abyad. The Turks will be allowed to retain control there. Turkey's military says the US has told it that all Kurdish fighters have now left that area.

It also does not include the area around Qamishli. The memorandum of understanding between Turkey and Russia makes the Kurdish-majority city an exception but gives no details as to why.

What else is in the deal?

After the deadline for the Kurdish fighters to withdraw expires on 29 October, Turkish and Russian troops will begin joint patrols in areas described as "in the west and the east of the area" of the Turkish offensive.

The statement from Russia and Turkey also says Kurdish forces "will be removed" from Manbij and the town of Tal Rifat, 50km to the west of Manbij.

On Wednesday, Russia's defence ministry said the Syrian government would establish 15 border posts with Turkey.

What has been the response to the deal?

Kurdish militias and political leaders have made no comment on whether they will agree to the demands.

Kremlin spokesman Dmitry Peskov said if the Kurds did not retreat, the Syrians and Russians would fall back and leave them to face "the weight of the Turkish army".

Syria's President Bashar al-Assad has in the past raised concern about foreign interference in Syria, but the Kremlin said he had thanked President Putin and "expressed his full support" for the deal.

 Families have been fleeing in the Syria-Turkey border region

Iran's foreign ministry said the agreement was a positive step and that it backed any move to restore stability in the region.

Nato Secretary-General Jens Stoltenberg said on Wednesday it was too early to judge the deal, and called for a "real, negotiated, political solution in Syria".

The US ambassador to Nato, Kay Bailey Hutchison, said the US backed Germany's plan for an internationally controlled security zone in the area, although she said direct US involvement was unlikely.

In Geneva on Wednesday, a Syrian Kurdish man set himself on fire outside the HQ of the UN's refugee agency and is now being treated for his injuries.

How did we get here?

A US-led coalition relied on Kurdish-led forces to battle IS militants in northern Syria over the past four years, but they are dominated by the Kurdish People's Protection Units (YPG) militia, which Turkey sees as a terrorist organisation.

Just over two weeks ago President Donald Trump announced that he would be withdrawing US troops from Syria. Soon after, Turkey launched an offensive against the Kurdish forces.

Russia stationed troops near the border over concerns that Syria's territory was being encroached upon by a foreign power.

Turkey agreed to pause its assault last week at the request of the US to "facilitate the withdrawal of YPG forces from the Turkish-controlled safe zone".

The ceasefire has largely held, despite what US officials described as "some minor skirmishes".

It had been due to expire on Tuesday evening but after the latest deal, Turkey said there was "no need" to re-launch its offensive.

What has the cost been?

The UN says more than 176,000 people, including almost 80,000 children, have been displaced in the past two weeks in north-east Syria, which is home to some three million people.

Some 120 civilians have been killed in the battle, along with 259 Kurdish fighters, 196 Turkish-backed Syrian rebels and seven Turkish soldiers, according to the Syrian Observatory for Human Rights (SOHR), a UK-based monitoring group.

Twenty civilians have also been killed in attacks by the YPG on Turkish territory, Turkish officials say.