GEVGELIJA, Macedonia (AP) — Thousands of tired and beleaguered migrants — mostly Syrians, Iraqis and Afghans fleeing conflict — boarded trains and buses in Macedonia that took them one step closer to the European Union on Sunday, a day after they stormed past police trying to block them from entering the country from Greece.

On Saturday, some 2,000 rain-soaked migrants rushed past baton-wielding Macedonian officers, who had been sealing the border for three days. Police fired stun grenades and dozens of people were injured as the migrants leapt over barbed wire or ran across a field not protected by the fence to enter Macedonia.

After the incident, police decided to allow migrants to cross the border freely again from Greece, which is also overwhelmed by the human tide. Police officials said that the blockade was imposed to try and stem the overflow of people that has caused chaotic scenes at a railway station in the Macedonian town of Gevgelija as thousands tried to secure places on overcrowded trains.

On Sunday, the migrants — many with small children and babies — orderly boarded trains and buses that took them to the border with Serbia before heading farther north toward EU-member Hungary, which is building a razor wire fence on its frontier to prevent them from entering. If they manage to enter Hungary, the migrants could travel freely across the borders of most of the 28 EU-member states.

Thousands of migrants who reached Serbia overnight faced an overcrowded refugee center where they have to apply for asylum — the paper that allows them three days to reach Hungary.

Emina, a migrant from Syria who boarded an early morning train with her two-month-old baby, blamed Macedonian authorities for "harassing" the migrants, not giving them food or water, as well as holding them back at the border.

"It was very hard in Macedonia," she said. "I did not sleep or eat for three days. Just as we arrived to the border, they closed it. It was awful."

Both Greece and Macedonia have seen an unprecedented wave of migrants this year. More than 160,000 have arrived so far in Greece, mostly crossing in inflatable dinghies from the nearby Turkish coast — an influx that has overwhelmed Greek authorities and the country's small Aegean islands. Some 45,000 crossed through Macedonia over the past two months.

Few, if any, want to remain in Greece, which is in the grip of a financial crisis, or impoverished Macedonia. Most of the migrants who enter from Greece want to head straight to Macedonia's northern border and then north through Serbia and Hungary on their way to more prosperous EU countries such as Germany, the Netherlands or Sweden.