The man, believed to be Moroccan, was among some 1,500 people, mostly from Pakistan, Iran and Morocco, stuck near the northern Greek border town of Idomeni, demanding to cross into neighboring non-EU Macedonia and then on to northern Europe.
His badly burnt body was lying next to railway lines, a Reuters witness said. Earlier, Macedonian police fired tear gas at protesting migrants who pelted them with stones.
Overwhelmed by hundreds of thousands of people streaming into Europe this year, Balkan states began blocking passage last month to all but Syrians, Iraqis and Afghans, who are regarded as refugees because they are fleeing conflict.
Macedonia has erected a metal fence to keep others out.
Violence broke out on Saturday after another man, also believed to be Moroccan, was badly burned when he climbed on top of a train wagon and was electrocuted.
Several hundred migrants blocked the crossing for refugees in protest late on Wednesday, shouting: "If we don`t cross, no one does!"
While deaths at sea are common, Thursday`s death was the first casualty at the Greek-Macedonian land border. More than 3,000 people have drowned trying to reach Europe on packed, flimsy boats this year. Many more bodies are never recovered.
The Greek government says it is trying to persuade the those stuck at the border in squalid camps and in near-freezing temperatures, to come to Athens and apply for asylum in Greece, saying there was accommodation available for them.
Migrant dies on Greek-Macedonian border in second day of clashes
03 December 2015
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A migrant was electrocuted to death at the Greek-Macedonian border on Thursday during a second successive day of clashes between police and migrants stranded for weeks on the Greek side.
