ISTANBUL — The Turkish government said Monday that one of its fighter planes shot down a Syrian military helicopter that had flown into Turkish airspace, a potentially significant escalation of tensions between the neighbors and former allies, now bitterly divided over Syria’s civil war.

An F-16 warplane intercepted a Russian-built Mi-17 helicopter as it crossed Turkey’s southern border, Turkish officials said. The helicopter’s crew was repeatedly warned by radio and did not turn back, they said. When the helicopter had strayed roughly a mile across the border, the jet fired on it, the officials said, and it crashed to the ground in Syria.

“No one, from now on, will dare to violate Turkish borders in any way,” the Turkish foreign minister, Ahmet Davutoglu, told reporters in Paris on Monday evening, according to the semiofficial Anatolian News Agency.

The Syrian Army confirmed that it had lost a helicopter that it said was on a reconnaissance mission and had mistakenly crossed into Turkish territory.