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After Turkey declared it would open its 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. His decision 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.

After his speech, thousands began making their way towards the European 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).

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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.

Elsewhere, Erdogan's communications director, Fahrettin Altun, tweeted Sunday nearly 81,000 people left Turkey for Europe in the past several days.

"This number may increase in the following days," he added.

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.

Greece placed its borders on maximum security footing on Sunday.

At least 500 people had arrived by sea on three Greek islands close to the Turkish coast within a few hours on Sunday morning, police said.

On the mainland further north, migrants waded across a river to the Greek side at Kastanies. Reuters reporters saw groups of up to 30, including an Afghan mother with a five-day old infant, on the side of a road, having forded the river hours earlier.