Turkish fighter jets on patrol near the Syrian border on Tuesday shot down a Russian warplane that Turkey said had ignored numerous warnings and violated its airspace, in a long-feared escalation that will further strain relations. NATO announced that it would hold an emergency meeting on Tuesday in Brussels to discuss the episode, as credible reports were emerging from Latakia Province, where the Russian jet went down, that rebels possibly wielding TOW antitank missiles and other weapons had hit a Russian helicopter sent to the scene of the crash to look for survivors. In his first remarks on the incident, President Vladimir V. Putin of Russia confirmed that an F-16 Turkish fighter jet had shot down the Russian plane, a Sukhoi Su-24, with an air-to-air missile. But he insisted that the Russian jet had been in Syrian airspace at the time.