By Babak Dehghanpisheh and Bozorgmehr Sharafedin

BEIRUT/DUBAI (Reuters) - Iran’s Islamic Revolutionary Guard Corps was quick to condemn the execution of Saudi cleric Sheikh Nimr al-Nimr, stating: "Without a doubt, the hated Saudi regime will pay a price for this shameful act."

For an organization deeply involved in wars in Syria and Iraq this looks no idle threat, at least in the eyes of Sunni Gulf Arab states like Saudi Arabia who say Shi'ite rival Tehran is bent on undermining their security.

The Guard's furious comment is not a call for direct conflict with Riyadh, something neither country wants. But it is a reminder to Gulf Arabs that the IRGC, with connections in Saudi Arabia and elsewhere in the region, has many ways to wage the long cold war between Tehran and its Arab foes.

Tehran denies interfering in Arab lands. But the Quds Force, the arm of the Guards that operates abroad, has contributed fighters, weapons and military supplies to back Iran’s interests and policies across the region.

That prospect is worrying for a region where conflicts or political crises from Lebanon and Syria to Yemen, Iraq and Bahrain involve proxies of both powers who are at daggers drawn.

A day after the IRGC issued its statement, which described Saudi rulers as "terrorist fostering, hated and anti-Islam", Riyadh broke off diplomatic relations with Tehran, escalating a contest for power that underpins the region's turmoil.

There is no firm indication that Iran's factionalized leadership has agreed how far it should go to avenge the death of Nimr -- who was one of 47 people executed by Saudi Arabia on Saturday -- and what methods should be used. But whatever steps are authorized, the Guards are likely to be involved, although as orchestrators more than direct participants, experts say.

"The Guard will not respond directly," said Hilal Khashan, a professor of political science at the American University of Beirut.

RIVALRY

"They have their operatives, their people, their connections everywhere in the region who will answer what the Saudis did and actually escalate. Iran is in a very strong position to respond in the Saudi Arabian eastern province. And they can do a lot in Bahrain."

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Moderate voices on both sides do not have an interest in seeing the situation escalate into a full conflict, experts say.

And yet the rivals often compete indirectly through allies, which lends the contest an element of unpredictability: Some Iranian proxies may be encouraged by the tough rhetoric coming from Tehran to carry out attacks not sanctioned by the Guard.

"Both sides are loath to see tensions spiral out of control. They are more likely than not to prevent this cold conflict from deteriorating into a hot one, while stepping up their proxy wars across the region," said Ali Vaez, the senior Iran analyst at the International Crisis Group.

"But with tensions reaching new heights, now more than ever, they run the risk of unintended direct confrontation."

The Quds Force has gained valuable military experience in recent years and now plays a dominant role within the IRGC, experts say. In some cases, Guard fighters and their Shi’ite proxies have fought against Sunni groups directly supported by Saudi Arabia in Syria and Iraq.

The IRGC has also established intelligence networks among the Shi'ite populations in the Gulf states. It has the potential to undermine Saudi Arabia and its allies' interests using sympathetic Shi'ites to stir political unrest or engage in violent attacks, experts say.

Saudi Arabia has a sizable Shi’ite community in the east of the country, while the majority of Bahrain’s citizens are Shi’ites who live under a Sunni monarchy. A failed uprising which began in Bahrain in 2011 was largely focused on gaining more democratic rights for the country’s Shi’ites.

In the Guards' statement, they warned that the youth and Muslims of Saudi Arabia would take "tough revenge" which would lead to the fall of the Saudi government. The Iranians could also revive the resentment that drove the Bahrain uprising.

RED LINE

"I think the Iranians think they can actually have a victory in Bahrain which would be a red line for the Saudis,” said a Western diplomat in Beirut who asked not to be identified.

"A key part of the Iranian narrative is that Bahrain is a majority Shi’ite nation that is being oppressed and not allowed democracy."

The bulk of Iran's tough rhetoric has come from hardline groups like the Guards, some of whom have also criticized the nuclear deal agreed with world powers last year aimed at lifting most sanctions against the country.

More diplomatic isolation is not good news for pragmatic Iranian President Hassan Rouhani who, with the blessing of Supreme Leader Ayatollah Ali Khamenei, pushed for the deal in order to expand Iran's ties with the international community.

Rouhani managed to normalize ties with the West somewhat through the deal and started the new year with an optimistic tweet hoping that in 2016 countries can "look for reasons to make peace, not excuses for hostility".

But now facing the biggest diplomatic crisis of his government, Rouhani might not be able to persuade the Guards to dial down their paramilitary activism in favor of diplomacy.

That could lead the Guards to push their allies within Saudi Arabia to carry out violent attacks.

"Should the IRGC desire to use terrorism on Saudi soil to retaliate against the House of Saud, the IRGC is likely to find it easier to find recruits among the Shia in Saudi Arabia," said Ali Alfoneh, a senior fellow at the Foundation for Defense of Democracies and an expert on the Revolutionary Guards.

It is unlikely the Guards would do much to hit Saudi interests in Syria or Iraq. But harsh anti-Saudi rhetoric from Iran may spur some of the militias trained and armed by Tehran to act on their own, experts say.

ANGRY MILITIAMEN

"Iran has created a Frankenstein with the Shi’ite militias in Iraq," said the Western diplomat in Beirut.

"When you keep emphasizing this notion of Saudi Arabia and its proxies oppressing Shia -- and you’ve got these angry militiamen -- at some point they’re going to be out of Iran’s control. There’s always the risk of that kind of escalation."

For their part, the Saudis could boost their financial and military support to Sunni militant groups in Iraq, Syria and Lebanon to counter the Iranian threat, experts say.

Still, it would be difficult for the Saudis to prevail in a political and diplomatic showdown with Iran, experts say.

"The fact that the Saudis have decided to sever their diplomatic relations with Iran means that they are, in their own minds, ready for an all-out confrontation with Iran," Khashan said. "There is nothing the Saudis can do to destabilize Iran whereas the Iranians on the other hand have every means conceivable to destabilize Saudi Arabia and other Gulf countries, namely Bahrain."

(Reporting by Babak Dehghanpisheh in Beirut and Bozorgmehr Sharafedin in Dubai; Editing by William Maclean and Giles Elgood)