ATHENS, Greece (AP) — All it took was a thinly veiled suggestion by a Turkish official that his country would no longer prevent migrants and refugees from trying to cross Turkey’s borders into the European Union. Within hours, thousands were heading from Istanbul to the Greek border, about three to four hours’ drive away.

By the time Turkish President Recep Tayyip Erdogan officially announced the borders were open Saturday, Greek authorities — who by no means intended to open their own border — had been playing a cat-and-mouse game with migrants attempting to break through the frontier. They fired tear gas and stun grenades to thwart efforts to push through the border by groups of migrants hurling rocks and pieces of wood.

After a mostly quiet day Sunday, violence erupted again Sunday afternoon. One policeman suffered facial injuries. Greek authorities said Turkish authorities also fired tear gas at the Greek border.

Greece said about 10,000 attempts to cross through its land border had been thwarted Saturday, and another 5,500 between Sunday morning and evening. Most of those gathered on the border were young Afghan men, although there were also families with young children and people from other countries.

Hundreds of others took advantage of good weather to make the short but often perilous sea crossing from the Turkish coast to offshore Greek islands. There, most were from Afghanistan and Africa.

Island residents are already angered by government plans to build new migrant detention centers there to ease severe overcrowding in the existing facilities.

On the island of Lesbos, some residents prevented new arrivals, who included families with young children and babies, from disembarking from a dinghy that arrived in a small harbor. Others blocked the road to the island’s main migrant camp, preventing buses from picking up groups who had arrived in other parts of the island.

Turkey's decision to ease border restrictions came amid a Russia-backed Syrian government offensive into Syria's northwestern Idlib province that has killed dozens of Turkish troops and led to nearly a million Syrian civilians fleeing toward Turkey's sealed border.

Turkey backs the Syrian rebels fighting in Idlib.

A Turkish official said the fighting in Idlib was directly linked to Turkey's opening the gates to Europe, saying Ankara had changed its focus to preparing for the possibility of new arrivals from Syria “instead of preventing refugees who intend to migrate to Europe.”