"We're concerned about these vulnerable people who are exposed to the elements," said U.N. migration agency's Turkey chief said.
After Turkey declared it would open it's land border with Greece, at least 13,000 people have gathered there hoping to cross into the European Union, the United Nations migration organization said Sunday.
Spurred on by Saturday's announcement from Turkish president Recep Tayyip Erdogan that he would not "close these doors in the coming period," thousands made their way border.
In return for E.U. funds, Turkey agreed to step up efforts to halt the flow of hundreds of thousands refugees passing through the country and into Europe, mainly via Greece and Bulgaria in 2015.
However, Erdogan accused the E.U. of not keeping up it's end of the bargain.
After his speech, thousands began making their way towards the border. Buses were being loaded to over-capacity with people bound for the border area, according to the U.N.'s International Organization for Migration (IOM).
Staff working along the 130-mile long border between Turkey and Greece and in the capital had observed as of Saturday evening at least 13,000 people gathered at the formal border crossing points at Pazarkule and Ipsala and multiple informal border crossings, the IOM said in in a release.
Their numbers ranged between several dozen and more than 3,000, it added.
"Most of those on the move are men but we are also seeing many family groups traveling with young children," the IOM's Turkey chief, Lado Gvilava said.
Warning that temperatures were dropping to "near zero", he added: "We're concerned about these vulnerable people who are exposed to the elements."
The agency said its staff were tracking the movement of people and providing humanitarian assistance to the most vulnerable.
Greek authorities fired tear gas and stun grenades through Saturday to prevent repeated attempts by a crowd of more than 4,000 people massed at the border crossing in Kastanies to cross.
They also fought a cat-and-mouse game with groups cutting holes in a border fence along the border to crawl through.
Others were making the short, but often perilous sea crossing from the Turkish coast to the Greek islands.
At least three dinghies carrying migrants arrived on the Greek island of Lesbos Sunday morning.
The Greek government reiterated its promise to keep migrants out Saturday, and the country's Prime Minister Kyriakos Mitsotakis tweeted: "I want to be clear: no illegal entries into Greece will be tolerated. We are increasing our border security."
In a second tweet, he added: "Greece does not bear any responsibility for the tragic events in Syria and will not suffer the consequences of decisions taken by others."
Turkey's decision to open the borders with Greece came amid a military escalation in northwestern Syria's Idlib province that has forced hundreds of thousands of Syrian civilians to flee fighting there, with many of them heading north toward Turkey.