Hundreds of migrants and refugees walked out of an overcrowded camp on the Greek-Macedonian border Monday, determined to use a dangerous crossing to head north.

More than 300 people, including dozens of children, were heading west toward a river that crosses the border, about five kilometres outside the village of Idomeni, where some 14,000 people are stranded at a sprawling camp.

They refused to turn back at a Greek police cordon outside the camp.

More than 40,000 people have been stranded in Greece after Macedonia and other ex-Yugoslav countries closed their borders to migrants and refugees — prompting them to seek more dangerous crossings.

Underscoring the risks, police in Macedonia said the bodies of two men and one woman, believed to be migrants, were found Monday in the Suva Reka river near the border with Greece. Twenty migrants crossed safely and another three were hospitalized, authorities said.

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

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

Greece Migrants

Migrants walk through a field north of Idomeni, Greece, attempting to reach Macedonia on a route that would bypass the border fence on March 14, 2016. (Visar Kryeziu/AP)

The UNHCR says Turkey must do more to ensure that all people seeking asylum there can have their claims efficiently assessed within a fair period of time, examining the European Union's planned deal with Ankara to send thousands of migrants in Greece back to Turkey, which they hope to finalize by Friday.

It said agreements like this one should "be guided and framed by international and regional obligations, to ensure their sustainability and respect for the rights of affected individuals." 

It noted that Turkey is home to 2.7 million Syrian refugees, only 10 per cent of them sheltered in camps.

Macedonia steps up border patrols

Police and armed forces on the Macedonian side of the border have stepped up patrols along parts of the newly-built border fence where migrants are likely to cross.

Parts of the fence are 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 east 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 8,500 refugees and migrants travelled to the Greek islands from Turkey last week, according to the UNHCR.

APTOPIX Greece Migrants

A child wrapped in a plastic bag waits along with adults for donated tea while standing on a beam placed on the muddy ground at the northern Greek border station of Idomeni on Monday. (Vadim Ghirda/Associated Press)

In an interview published Sunday, Austria's foreign minister said border closures should be extended.

Sebastian Kurz told Germany's Bild am Sonntag 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."

Desperate migrants turn to smugglers

Stranded migrants have been desperate to continue their journey, with many seeking help from people smugglers. Hundreds crossed into Macedonia from Greece on Monday, defying the blockade.

Serbian customs officer at the border with Macedonia found 33 migrants hidden in a cargo train in an attempt to cross into the country illegally.

The customs office said Monday that the group was discovered on Saturday in three wagons at the end of an empty train that had arrived from Macedonia.

The statement says the migrants included one woman. It says the migrants were aged 18 to 26 and had no documents but said they were from Afghanistan, Libya and Syria. They have been handed over to police.