IDOMENI, Greece – Scuffles and limited fights broke out Friday among more than 1,000 people at Greece’s northern border with Macedonia as exhausted, thirsty migrants jostled to get into position to cross.

Macedonian authorities were allowing up to 50 people across at a time Friday from the Greek village of Idomeni, but more were arriving by the busload all day.

Once across, the migrants board trains or buses north to Serbia in their quest to reach more prosperous European countries such as Germany, Sweden and the Netherlands and ask for asylum.

A Greek policeman on the border estimated about 1,000 people were crossing in an eight-hour period each day. The officer spoke on condition of anonymity because he was not authorized to speak publicly.

About 300 of those waiting had arrived the previous day and spent the chilly night in the open, lighting small fires to keep warm. Aid organizations including Doctors Without Borders were providing medical help, shelter, food and water.

Most of those at Idomeni were from Syria and Afghanistan, while others were from Iraq, Iran, Pakistan and Bangladesh. The vast majority had arrived on treacherous but brief sea journeys to Greece’s eastern Aegean islands in inflatable dinghies from the nearby Turkish coast.

Nour Kady, a 30-year-old Syrian, had paid $2,200 to Turkish smugglers for the two-hour boat trip to the island of Lesbos for himself, his wife and their 1-year-old son. The trip, he said, was harrowing, with 60 people crammed into the nine-meter (29-foot) dinghy.

“It was night, we set out at 2am, the sea was rough, there were big waves,” Kady said. “This trip was very difficult.”

His family was among the thousands now arriving on Greek islands each day. So far this year, 200,000 people have entered Greece, according to figures released Friday from the U.N. High Commissioner for Refugees. Italian officials say another 110,000 migrants have entered Italy.

Many in Idomeni had attempted the sea crossing several times before being successful.

“We tried three times to cross into Greece,” said a university professor from the Syrian city of Aleppo, who did not want to give his name for fear of reprisals against family members in Syria.

On his first attempt, he paid a smuggler to take his family from the Turkish city of Izmir to the departure point on the coast, but was arrested and sent back to the city, where he spent two days in jail.

The second attempt also ended in arrest, although without being sent to jail.

“The third time we managed to get into a boat. There were more than 45 people (on it) and the waves were big. The boat was taking on water, but we managed to reach Samos,” a Greek island near the Turkish coast, he said.

“A fisherman on the coast saw us and got into the water and pulled us out. He was a good man,” he said.

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