Some 13,000 migrants have gathered along the Turkish-Greek border after Turkey's president threatened to allow some of the some 3.6 million refugees in the country cross into Europe, the UN said Saturday.

"Thousands of migrants, including families with young children, are passing a cold night along the border between Turkey and Greece," the International Organization for Migration said in a statement.

The UN agency said its staff had been tracking the movement of people from Istanbul and were providing humanitarian assistance to the most vulnerable.

"By Saturday evening, staff working along the 212-kilometre-long border between Turkey and Greece and in the capital had observed at least 13,000 people gathered at the formal border crossing points at Pazarkule and Ipsala and multiple informal border crossings," it said.

The agency said it had spotted "groups of between several dozen and more than 3,000.

"The number of migrants moving through Edirne towards the border grew through the day as cars, taxis and buses arrived from Istanbul," the head of IOM's Turkey mission Lado Gvilava said in the statement.

"Most of those on the move are men but we are also seeing many family groups travelling with young children," he added.

Gvilava said the IOM was distributing food and other basic supplies, but with temperatures dropping close to freezing "we're concerned about these vulnerable people who are exposed to the elements."

IOM staff reported that buses continued into the evening to be "loaded to over-capacity" in Istanbul with people bound for the border area.

The mass movement of people began after Turkey's President Recep Tayyip Erdogan threatened to open the gates and allow refugees to travel to Europe as a way to pressure EU governments over the Syrian conflict.

Turkey and Russia, who back opposing forces in the Syria conflict, have held talks to defuse tensions after an air strike killed the Turkish troops, sparking fears of a broader war and a new migration crisis for Europe. 

At the border Saturday, Greek police clashed with several thousand migrants already gathered at the entrance to EU territory, where they hurled rocks at security forces firing tear gas across the frontier. 

In 2015, Greece became the main EU entry point for one million migrants, most of them refugees fleeing the Syrian civil war.