Hundreds of migrants were back in Greece Tuesday, returned by Macedonian authorities a day after they left a refugee camp in Greece and crossed the sealed border.

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

Between 700 and 2,000 people from the refugee camp at Idomeni on the Greek side of the border on Monday waded through a river to walk around the fence, which Macedonia had erected to keep them out.

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

The countries lie on the Balkan route, which has become the favoured route of migrants trying to reach wealthy countries in the European Union after arriving in Greece from Turkey.

The move, preceded by a series of restrictions to slow the migration flow, 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 stuck for days and weeks, though facilities were set up for no more than 2,000, with no one expected to remain for more than a brief stay.

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

Their hopes of continuing north legally snuffed, hundreds took the offer of Greek authorities to relocate to better conditions in camps further from the border.

However most remained. And then there were some, such as the group on Monday, who attempted to cross the border by following the fence until it ended after a four-hour walk to the west.

The hike involves a walk across a small, but swollen and fast-running river Crna Reka. Three Afghans drowned when a group of Afghans attempted the journey in the night between Sunday and Monday.

EU Migration Commissioner Dimitris Avramopoulos was headed to Idomeni for a visit Tuesday, a spokesman wrote on Twitter.

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