The migrants, who had set off from an overcrowded Greek refugee camp several hours earlier, waded through a surging river as they found an alternative route north into Macedonia, bypassing the closed regular border crossing.
About 20 journalists who had followed the migrants from the Idomeni migrant camp were taken to a police station in Gevgelija, just over the border in Macedonia.
As thousands of refugees scramble to find ways past the Balkan blockade, three Afghans drowned in a rain-swollen river in Macedonia, while the Greek coastguard was searching for eight migrants missing in the Aegean.
Over 14,000 people have been stranded at Idomeni in increasingly desperate conditions after the main route to western Europe through the Balkans -- taken by over one million migrants since the start of 2015 -- was effectively shut down last week.
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Today some 1,000 migrants set off on foot in search of an alternative route into Macedonia, marching from Idomeni to the village of Chamilo some two kilometres away, closer to the sealed frontier with Macedonia.
But twice they managed to get round Greek police, the first time because there were too many of them, the second time because police vehicles could not follow the migrants into the river.
But they were later stopped by Macedonian troops and the journalists travelling with them taken to a police station.
On Twitter, a group using the hashtag #Marchofhope posted photos of people wading through water, with children on parents' shoulders.
Gevgelija is just over the Konska river which runs parallel to the Greek-Macedonian border.
British volunteer Matthew Sheppard said some of the migrants were getting desperate.
"We all know that the only real solution is for war to stop, to cut off the head of the snake. Here we are only doing damage control...We are just trying to put out a fire."
Earlier Monday, three Afghan migrants, including a pregnant woman, were found drowned in a river swelled by heavy rain as they tried to cross into Macedonia from Greece, the Macedonian interior ministry said.