KASTANIES, Greece — Thousands of migrants and refugees massed at Turkey’s western frontier Sunday, trying to enter Greece by land and sea after Turkey said its borders were open to those hoping to head to Europe. In Syria, Turkish troops shot down two Syrian warplanes after the Syrian military downed a Turkish drone, a major escalation in the direct conflict between Syrian and Turkish forces. Turkey’s decision to ease border restrictions came amid a Russia-backed Syrian government offensive into Syria’s northwestern Idlib province. That offensive has killed dozens of Turkish troops and led to a surge of nearly a million Syrian civilians fleeing the fighting toward Turkey’s sealed border. Turkey backs the Syrian rebels fighting in Idlib province, and has sent thousands of troops into the area. Idlib is the last opposition-held stronghold in Syria, and is dominated by al Qaeda linked fighters. A Turkish official said the fighting in Idlib was directly linked to Turkey’s decision to open the gates for refugees to Europe. He said 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.” “Europe and others must take robust action to address this monumental challenge,” said Fahrettin Altun, the communications director for Turkey’s President Recep Tayyip Erdogan. “We can’t be expected to do this on our own.” Erdogan’s announcement marked a sharp departure from the previous policy of containment, an apparent attempt to pressure Europe into offering Turkey more support in dealing with the fallout from the Syrian war to its south. In 2016, Turkey agreed to stem the tide of refugees to Europe in return for financial aid. Turkey already hosts 3.6 million Syrian refugees, as well as others from Africa,...