MOSCOW — Ratcheting up the confrontation over the Syria war, Russia said Monday that its “volunteer” ground forces would join the fight, and NATO warned the Kremlin after at least one Russian warplane trespassed into Turkey’s airspace.

The saber-rattling on both sides reflected a dangerous new big-power entanglement in the war, as longstanding differences between Russia and the United States over President Bashar al-Assad of Syria and his opponents increasingly play out not only in the halls of the United Nations but on the battlefield in Syria.

Russia squared off with Turkey and its NATO allies, calling the air incursion on Saturday an innocent mistake because of foul weather — a claim American officials rejected.

News services said late Monday that a second airspace violation might have been committed on Sunday, but that report could not be immediately confirmed.