BELGRADE (Reuters) - Serbia’s centers for housing migrants are completely full, the U.N. refugee agency said, leaving more than a thousand facing a winter sleeping rough in the Balkan country that has become a bottleneck as the European Union sealed its borders.

At least 7,000 migrants mainly from Afghanistan, Iraq and Syria are trapped in Serbia, many spending months in a country culturally and financially ill-equipped to care for them and where few of them want to stay.

Despite the official closure of the so-called Balkan route, which has eased pressure on rich nations like Germany, aid agencies estimate more than 100 new migrants are entering Serbia every day, while only around 20 are allowed to enter Hungary - Serbia’s only neighbor in Europe’s Schengen visa-free area.

About half of those are children, and every 10th child is classified as unaccompanied, a spokeswoman for Save the Children told Reuters at an overcrowded Belgrade center where the international NGO encourages children to take part in activities to help them come to terms with their trauma.

Serbia has pledged to make 6,000 beds available and has reached almost that total but has appealed for more help from the European Union to help it ease the crisis.

“All the reception centers are full, full,” a UNHCR spokeswoman said, adding that it was unclear whether Serbia would make any more capacity available.

The Serbian government agency for refugees and migration, the SRC, was not immediately reachable for comment.

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A warehouse in central Belgrade without basic facilities has become the home of more than 1,000 men - women and children are given priority in official camps - many of whom are reluctant to enter the system for fear their onward journey will be hindered.

It is one of the largest camps of its kind in a European capital. The site it occupies is due to become part of the Belgrade Waterfront project, a new luxury development being built by Emirati developer Eagle Hills.

“Serbia is becoming a buffer zone, some kind of purgatory,” said Rados Djurovic, executive director of the Asylum Protection Centre, a Serbian non-profit organization that provides legal and psychological support to displaced persons.

Many migrants are turning to people-traffickers to smuggle them into Hungary or Croatia, with the short Croatian border effectively sealed and a months-long waiting list at the barbed-wire Hungarian border.

Serbian authorities found 77 migrants hidden in two cargo vehicles on Monday. On Thursday, three Afghan migrants including a child died in a traffic accident in southern Serbia. The driver, a suspected people-smuggler, fled the scene.