Macedonia intermittently opened its border with Greece to a tiny trickle of Syrian and Iraqi refugees Wednesday, leaving about 10,000 more people camped on the Greek side, with more arriving daily.

The border bottleneck has left at least 25,000 people stranded in Greece, the first European country that migrants reach in smuggling boats from Turkey. As the prosperous but divided continent flails in search of a workable solution, individual countries led by Austria have imposed immigration caps that have caused a domino effect down the Balkan immigration corridor, which has been traversed by a million people over the past year.

Greek police say Macedonian police opened the Idomeni crossing three times Wednesday, each time for a few hours. They admitted a total of 240 people from Syria and Iraq — the only nationalities allowed to continue north.

Hundreds, including many families with small children, arrive daily at Idomeni in northern Greece, where two official camps are so full that thousands have set up tents in fields all around.

A father holds his child as he waits to enter Macedonia from Greece near the southern Macedonian town of Gevgelija, Wednesday. (Visar Kryeziu/Associated Press)

Greece has asked for 480 million euros in emergency aid from the European Union to deal with the crisis.

EU Humanitarian Aid Commissioner Christos Stylianides said Wednesday he wants to swiftly push through a proposal to earmark 700 million euros in humanitarian aid to deal with the refugee crisis over the next three years. He said 300 million euros would be earmarked for this year and be used "where it is most needed," alluding to Greece and the nations along the Balkan trail.

Macedonia says it will only allow in as many refugees as Serbia, its northern neighbour, accepts each day.

Slovakia's prime minister, Robert Fico, visited the Macedonian side of the border Wednesday and stressed the importance of bilateral cooperation in addressing the migration crisis.

"We all believe that we need to adopt European solutions, but sometimes it seems to us that European solutions do not work," he said. "So, probably, also bilateral cooperation, cooperation among countries, countries like Macedonia, are very, very important."

A field official with the United Nations refugee agency on the Macedonian side of the crossing said authorities will soon send a train with about 500 people from the nearby town of Gevgelija to the Serbian border. He spoke on condition of anonymity because he was not authorized to brief the media.

Refused entry

Jasmin Rexhepi, head of the aid group Legis, told The Associated Press that a group of about 50 Pakistanis remain trapped for a fourth day on the Macedonian side of the border between two razor-wire fences. He said Macedonian authorities are trying to send them back to Greece because the group crossed the border illegally.

Rexhepi also said that about 1,000 refugees — 750 Afghans and 250 Iraqis — are stuck at Macedonia's border with Serbia, which has refused them entry.

In Greece, arrivals by smuggling boats from Turkey on the eastern Aegean Sea islands continue at a rate of nearly 2,000 a day. More than 120,000 have landed so far this year, on top of 850,000 in 2015. A string of hastily thrown-up transit camps on the mainland has rapidly filled up, and hundreds are sleeping rough in a central Athens square.

Authorities have restricted the flow of migrants from the islands to Athens' port of Piraeus, where about 1,000 people still arrived by ferry by midday Wednesday.