Around 2,000 people from the Greek refugee camp in Idomeni on Monday waded through the river where three migrants had drowned earlier that day, in a bid to reach the sealed Macedonian border.
The group has arrived in Moine, five kilometres to the west on the Macedonian side of the border, TV Sitel reported in Skopje. Macedonian authorities were mulling how to return the people back to Idomeni, it said.
The travelling group encountered Greek police, which did not attempt to stop them, but advised them that they would be returned by Macedonian police waiting on the other side.
A reporter said the group walked for four hours to skirt the three-metre border fence laced with razor wire, which was constructed by Macedonia in recent months to control the migration flow.
People helped each other cross the small river Crna Reka, swollen after days or relentless rain, where three Afghan migrants drowned hours earlier while trying to sneak into Macedonia.
The victims were part of a 26-member group trying to cross the border, which Macedonia sealed to migrants last week, causing a massive backlog of people on the Greek side.
More than 10,000 migrants, mostly Syrian and Iraqi refugees, have been stranded at Idomeni after Balkan countries first restricted, then stopped the flow of migrants towards wealthy EU countries.
Aid organizations have voiced concern that stifling the regulated migration flow could lead to the smuggling of people and potentially dangerous attempts at illegally scaling borders.
In the Aegean Sea, meanwhile, rescuers were searching for eight migrants missing after their boat overturned in the rough sea early Monday morning.
Greek coastguard spokesman Nikos Langadianos told national TV that five people were rescued near the island Kos, as vessels from the Greek and Italian coastguard - assisted by a helicopter - searched the sea for survivors.
Greek Aegean islands last year became the main gateway for migrants, including Syrian and Iraqi refugees, trying to reach Europe from Turkey.
At least 455 have drowned in the Aegean Sea this year alone, according to data from the International Organization for Migrations.
More than 995,000 people have made the eastern Mediterranean crossing since 2015, 139,000 of them since the start of the year, the UN refugee agency (UNHCR) reports.
From Greek islands, the people are ferried to Athens, then had typically continued their trip north and west, through Macedonia, Serbia, Croatia, Slovenia and Austria.
Countries on the Balkan route have been gradually restricting the flow, first stopping all but Syrians and Iraqis and, eventually, starting March 9, barring entry to all.
The European Union is now negotiating a deal with Turkey to also stem the number of migrants and asylum seekers who attempt to cross the Aegean Sea, hoping to finalize it at a summit in Brussels this week.
The planned deal foresees Ankara taking back any new migrants arriving in Greece, while the EU would agree to directly resettling an equal share of Syrians living in Turkey.
The plan is meant to discourage migrants from putting their lives in the hands of smugglers, but it has faced a barrage of criticism from human rights advocates and high-ranking UN officials, who have called the approach inhumane and illegal.
On Monday, Spanish Foreign Minister Jose Manuel Garcia-Margallo joined the critics' ranks, saying that his country is seeking changes to the "unacceptable" agreement.
"Spain will only accept ... an agreement that is coherent, compatible and respectful of international law and extraordinarily respectful of the human rights of people who have to flee from their country," he said in Brussels on the margins of an EU foreign ministers' meeting.
He noted that any "collective expulsions" by the EU of migrants would be particularly problematic.
Madrid has given a mandate to its EU ambassador to seek a correction of the legal texts, Garcia-Margallo said. He added that anyone who arrives on European soil should be allowed to file an asylum request that should be assessed individually, with a right to appeal.