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In dramatic scenes, over 2,000 refugees carried their children and belongings through thigh-deep waters, helped by a human chain made up of many others in their predicament, to pass through one of the few remaining parts of the Macedonian border not yet sealed.

Since February, large numbers of refugees have lived in desperate conditions on the Greek-Macedonia border facing bolted-shut gates.

As the late winter rains lashed around them many could only watch as their temporary camps slowly turned into swamps.

But despite recent EU plans that sought to keep them from entering further into Europe, the refugees were not ready to give up on their journey.

Their move into Macedonia on Monday sparked an immediate reaction from Macedonian authorities who had long monitored them on the Greek side of the border.

Following their crossing, hundreds of migrants were detained and put into trucks by soldiers and police.

Their fate remains uncertain and the Macedonian police refused to give any further details.

Monday's events were the biggest challenge to border closures since the route from Greece to central Europe was sealed off 10 days ago, leaving over 40,000 refugees stranded in Greece.

Thousands of refugees crossed through the Macedonian border on Monday [Getty]

Syrian Ibrahim al-Almad said he had been stuck in Greece for a month.

"My brother is in Stuttgart, in Germany, and I want to join him," he said, pointing toward other refugees.

"Look at what they are making us do. Look at all these women and children."

Almad had walked from the Greek village of Idomeni, where 14,000 people remain camped out.

Underscoring the risks, police in Macedonia said the bodies of one man and two women were found on Monday in the Suva Reka river near the border with Greece.

Twenty migrants crossed safely and another three were hospitalised, authorities said.

"This is the situation in which people have become desperate and frustrated," said Ljubinka Brasnarska, a spokeswoman in Macedonia for the UN refugee agency UNHCR.

"The border restrictions imposed by the countries have forced people to take desperate actions."

A cap on migrants imposed by Austria last month set off a domino effect of border closures across the Balkans, leaving thousands stranded in Greece.

Parts of Macedonia's border fence is made up solely of coils of razor wire, while breaks in the barrier also occur at rivers and mountain slopes on the border, mainly to the west of Idomeni.

A cap on migrants imposed by Austria last month set off a domino effect of border closures across the Balkans, leaving thousands stranded in Greece.

Despite the closures, more than 8,500 refugees and migrants travelled to the Greek islands from Turkey last week, according to the UNHCR.

Refugees attempted to cross a river after leaving the Idomeni camp in Greece [Getty]

Austria's foreign minister urged on Sunday for border closures to be extended.

Sebastian Kurz told Germany's newspaper that the route leading through Italy to central Europe should also be blocked.

"Smuggling can't be prevented entirely [so] we will have to do everything that we are now doing on the western Balkan route along the Italy-Mediterranean route too," he said.

"The time of waving through refugees to central Europe is over."

Meanwhile, German chancellor Angela Merkel said on Monday she would stick to her course in Europe's migrant crisis following state elections that sent conflicting signals about German public opinion of her liberal approach and highlighted divisions in her conservative bloc.

Merkel acknowledged that Sunday's three elections, which produced painful losses for her conservative Christian Democratic Union, were dominated by the migrant issue and many voters believed there is "no conclusive and satisfactory solution."

However, "I am firmly convinced, and that wasn't questioned today, that we need a European solution and that this solution needs time," Merkel said after party leaders met in Berlin.

The nationalist, anti-migration Alternative for Germany, or AfD, surged into three state legislatures after campaigning against Merkel's welcome for last year's huge influx of migrants.

Last year, Merkel insisted that Germany will manage the challenge of integrating migrants as the country registered nearly 1.1 million people as asylum-seekers.

While her government has tightened asylum rules, she still maintains a pan-European solution to the migrant crisis, ignoring demands for unilateral national measures.

The largely liberal rhetoric remains in place, but other countries' border closures have lately reduced the migrant flow to a trickle and Merkel has made clear she does not plan to bring refugees now stuck in Greece to Germany. 

Despite that, Merkel criticised the unilateral border closures, and said on Monday "you can see every day from the photos from Greece that the solution isn't so sustainable yet."

Agencies contributed to this report.