IDOMENI, Greece (Reuters) – Hundreds of dejected migrants returned to a transit camp in northern Greece on Tuesday after Macedonian authorities blocked their attempt to cross the border or drove those who did get across back to Greece.

Around 2,000 migrants marched out of the Idomeni camp on Monday, hiking into the mountains and fording a river in what Greek authorities said was a well-planned attempt to find a way around a barbed wire fence built by Macedonia to keep them out.

Three migrants drowned on Monday trying to cross a river into Macedonia, one stage on a route that the migrants hoped would take them to Germany and other wealthy European Union countries.

Macedonia loaded about 1,500 migrants and refugees who had succeeded in crossing the border onto trucks and drove them back to Greece, Macedonian police said. Reporters and aid officials said the migrants were left at the Greek border.

Hundreds more migrants were prevented from crossing the border on Monday. Many of them streamed back to Idomeni on Tuesday after spending the night in the mountains.

Migrants carried children across a fast-flowing river before trudging back along muddy paths. One small child was dragged along on a blue plastic container attached to a rope.

“It’s a long way from the camp to the mountains, it took me six hours of walking. At my age it was very difficult,” said one of those returning, 60-year-old Mohammad Kattan.

Back in Idomeni, the camp was crowded, muddy and wet. People started fires to dry their clothes and to warm up. Several hundred migrants found shelter in a deserted farm in the area.

Greek officials said they could not confirm that Macedonia had sent back the migrants.

“No one has been returned from our official border crossings, and no request has been submitted by Skopje (the Macedonian capital),” said George Kyritsis, a spokesman for Greece’s migration coordination center:

Ties between the two neighbors are fraught because of Greece’s long-standing refusal to recognize Macedonia’s name, which is the same as that of a northern Greek province.

At least 12,000 people, including thousands of children, have been stranded in the Idomeni camp, their path to the EU blocked after Balkan nations closed their borders.

Greek Prime Minister Alexis Tsipras said on Tuesday there was “no chance” that borders which had been shut down throughout the Balkans would be re-opened. He urged refugees to move to reception centers set up by the state.

European Union leaders, trying to stem a flow of migrants and refugees fleeing war and poverty in the Middle East and beyond, are due to hold a new summit with Turkey this week to seal an agreement intended to halt the exodus.

Jan van’t Land, an official with medical charity Medecins Sans Frontieres at Idomeni, said around 400 migrants had returned to the camp.

“There are still many hundreds of people on both the Greek and the Macedonian side of the border,” he told Reuters.

EU Migration Commission Dimitris Avramopoulos, on a visit to Idomeni, urged EU countries to put into action immediately a long-stalled plan to re-house asylum seekers from Greece elsewhere in the bloc.

“Our aim is within the next two weeks to reach the level of 6,000 to be relocated every week,” he told reporters. “All our values are in danger today and you can see it here in Idomeni. I believe that building fences, deploying barbed wire, is not a solution.”

Conditions at the Idomeni camp have deteriorated after days of heavy rain. Concern about the spread of infection grew after one person was diagnosed with Hepatitis A.

(Additional reporting by Kole Casule in Skopje, Ivana Sekularac in Belgrade, Renee Maltezou and Karolina Tagaris in Athens, writing by Adrian Croft, editing by Larry King)