Macedonian authorities returned hundreds of migrants to Greece on Tuesday, one day after they set out from the Idomeni refugee camp and walked around a fence that Macedonia had erected to keep them out.

"Some 600-700 migrants who illegally entered Macedonia ... were returned to Greece," the Makfaks news agency reported, citing the Macedonian Interior Ministry.

As many as 2,000 people from the Idomeni camp on the Greek side of the border made the four-hour trek on Monday to the Macedonian side, wading through a river where three migrants had drowned earlier that same day.

Greek Deputy Defence Minister Dimitris Vitsas said Macedonia did not inform Athens that it would return the migrants.

"We know nothing about it," Vitsas told broadcaster TV Skai. "On the grounds of the Geneva conventions, it would be unlawful to send people back to Greece." 

The European Commission, the EU's executive, refused to comment on the legality of the move.

Last week Macedonia declared its borders closed to all travellers without valid passports and visas, matching similar measures from Serbia, Croatia and Slovenia.

The countries lie on the Balkan route, which is frequented by migrants trying to reach wealthy countries in the European Union after arriving in Greece from Turkey.

Macedonia's move was preceded by a series of restrictions to slow the migration flow and caused a massive backlog of people, many of them refugees from Syria and Iraq, in the Idomeni camp.

The crowd swelled to an estimated 14,000 at one point, most of them already stuck for days or weeks as facilities were set up to accommodate no more than 2,000 for a brief stay.

The deterioration of conditions at Idomeni was accelerated by unrelenting rain that turned the makeshift camp, with thousands of camping tents outside the original compound, into an ocean of mud.

With little hope of continuing north legally, hundreds took the offer of Greek authorities to relocate to better conditions in camps further from the border.

Most migrants, however, remained, and some attempted to cross the border by following the Macedonian fence to the west until it ended.

The hike involved crossing the small but surging river Crna Reka. Three Afghans, including a pregnant woman, drowned in their attempt to cross it in the night between Sunday and Monday.

On Tuesday, EU Migration Commissioner Dimitris Avramopoulos described the situation in Idomeni as "tragic" and a dishonour to the civilized world.

Europe's values "are in danger today, and you can see it here in Idomeni," Avramopoulos during a visit on Tuesday to the camp with Ioannis Mouzalas, the Greek minister in charge of migrant affairs.

Meanwhile, Greek Prime Minister Alexis Tsipras urged the people at Idomeni not to risk their lives in attempts to cross the sealed border and to accept a relocation offer. 

Migrant overcrowding spread beyond Idomeni as migrants continued to press into Greece from Turkey and none of them were allowed to continue to Macedonia and beyond.

By Tuesday, some 9,000 migrants - 2,000 more than on Sunday - had massed on Greek Aegean islands and were waiting for ferries to the mainland, TV Skai reported. 

Reception centres in the Athens area were already filled to their 4,000-person capacity, and several hundred people were due to be bussed out to other locations.

Athens estimates that there are around 46,000 migrants presently in Greece, and that the vast majority of them are refugees from war zones. 

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