By Ayla Jean Yackley and Humeyra Pamuk

ISTANBUL (Reuters) - The United States and its NATO allies denounced Russia on Monday for violating Turkish air space along the frontier with Syria, and Ankara threatened to respond if provoked again, raising the prospect of direct confrontation between the Cold War enemies.

NATO held an emergency meeting of ambassadors of its 28 member states to respond to what Secretary-General Jens Stoltenberg called "unacceptable violations of Turkish air space" after Turkey said a Russian jet had crossed its frontier.

NATO members "strongly protest" and "condemn" incursions into Turkish and NATO territory, the alliance said.

"Allies also note the extreme danger of such irresponsible behavior. They call on the Russian Federation to cease and desist, and immediately explain these violations," it said in a statement released after the meeting in Brussels.

Moscow's unexpected move last week to launch air strikes in Syria has brought the greatest threat of an accidental clash between Russian and Western forces since the Cold War.

Russian war planes and those of the United States and its allies are now flying combat missions over the same country for the first time since World War Two, with Moscow repeatedly targeting insurgents trained and armed by Washington's allies.

Turkey, a NATO member with the alliance's second biggest army, scrambled two F-16 jets on Saturday after a Russian aircraft crossed into its airspace near its southern province of Hatay, the Turkish foreign ministry said.

In a second incident, the Turkish military said a MiG-29 fighter jet - an aircraft used both by Russia and Syria's own air force - had harassed two of its F-16s by locking its radar on to them on Sunday as they patrolled the border.

Turkey summoned Moscow's ambassador to protest against the violation and said Russia would be held "responsible for any undesired incident that may occur" if it were repeated. Foreign Minister Feridun Sinirlioglu spoke with his Russian counterpart Sergei Lavrov, as well as key NATO partners.

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By Monday afternoon, Russia had not given its own public account of the incidents. Kremlin spokesman Dmitry Peskov confirmed that the Russian ambassador had been summoned and said "some facts were mentioned there which are to be checked", but gave no further details.

RULES OF ENGAGEMENT

Turkish Prime Minister Ahmet Davutoglu said he had been told by Russia that the violation was a "mistake" that would not happen again.

"Turkey's rules of engagement apply to all planes, be they Syrian, Russian or from elsewhere ... Necessary steps would be taken against whoever violates Turkey’s borders, even if it’s a bird," he said on HaberTurk TV.

"For Russia, which long opposed foreign intervention in Syria and blocked UN Security Council resolutions, to be actively involved in Syria is both a contradiction and a move that has escalated the crisis."

A senior U.S. defense official, speaking on condition of anonymity, said Washington doubted the incursions were an accident.

"We’re deeply concerned about it and consider it something that just contributes to our overall sense that there’s real strategic and tactical problems with the way Russia is conducting itself in Syria right now."

The United States and its allies are waging their own air campaign against Islamic State fighters in Syria, while demanding that Syrian President Bashar al-Assad step down and supporting other insurgents fighting against him.

Russia says it is targeting Islamic State, but the anti-Assad coalition including Washington, European powers, Turkey and most Arab states, say Moscow has mainly targeted other insurgents and hit few Islamic State targets.

The potential confrontation comes at a time when relations between Russia and the West are at their worst since the Cold War, with the United States and European Union having imposed financial sanctions on Moscow over its intervention in Ukraine.

Over the past year, NATO has repeatedly accused Moscow of sending planes to violate the air space of the alliance's member countries in Europe.

Speaking during a trip to Spain, U.S. Defense Secretary Ashton Carter compared Moscow's effort to bolster Assad to tethering itself to a sinking ship.

"By taking military action in Syria against moderate groups targets, Russia has escalated the civil war," Carter said in a speech in Madrid.

More than 40 Syrian insurgent groups, including some of the most powerful groups fighting against Assad and armed by Arab states, called on regional states to forge an alliance against Russia and Assad's other big foreign backer, Iran.

Regional cooperation was needed to counter "the Russian-Iranian alliance occupying Syria", they said. "Civilians have been directly targeted in a manner that reminds us of the scorched earth policy pursued by Russia in its past wars."

ENEMIES LIST

By infuriating Ankara, Russian President Vladimir Putin risks adding another name his costly and expanding enemies list: fast-growing Turkey is a big buyer of Russian gas and Moscow has announced ambitious plans to build pipelines across it to reach markets further west.

Turkey is one of Assad's fiercest foes in the region, has by far the biggest army on the border with Syria and has taken in the largest number of refugees.

President Tayyip Erdogan said Russia's defense of Assad was a "grave mistake".

"Assad has committed state terrorism, and unfortunately you find Russia and Iran defending (him)," Erdogan was quoted by the Hurriyet newspaper as telling a crowd of supporters in Strasbourg, France, late on Sunday.

"Those countries that collaborate with the regime will account for it in history," he said.

Britain's Foreign Secretary Philip Hammond said on Twitter: "(The) Russian incursion into Turkish air space raises stakes in what is already a high risk situation."

(Additional reporting by Maria Tsvetkova in Moscow, Phil Stewart in Madrid, Robin Emmott in Brussels; Writing by Nick Tattersall; Editing by Peter Graff and Giles Elgood)