DUBAI/CAIRO (Reuters) - Worsening enmity between rivals Saudi Arabia and Iran is jeopardizing peace prospects in Yemen where a nine-month-old war has given Islamist militants a foothold in Riyadh’s backyard.

A Houthi militant mans a weapon mounted on a patrol truck while securing a street where women are demonstrating against Saudi-led air strikes in Yemen's capital Sanaa January 21, 2016. REUTERS/Khaled Abdullah

Yemen’s principal warring factions -- fighters loyal to the ousted Saudi-backed Abd-Rabbu Mansour Hadi who are battling the Iran-allied Houthi militia and loyalists of former president Ali Abdullah Saleh -- held talks last month in Switzerland to try to end a war that has killed some 6,000 people.

They were due to meet again on Jan. 14 in a bid to seal a lasting peace. But the Riyadh government cut diplomatic ties with Shi’ite Iran in a row sparked by Saudi Arabia’s execution of Saudi Shi’ite cleric Sheikh Nimr al-Nimr on Jan. 2.

Shortly after the row in which the Saudi embassy in Tehran was stormed, the U.N.-brokered talks between the two opposing sides were postponed, with no clear date set to resume.

Saudi Arabia, a conservative Sunni Muslim monarchy, sees revolutionary Iran as the paramount threat to the Middle East’s stability, because of its support for Shi’ite militias that Riyadh says have inflamed sectarian violence.

For the Al Saud dynasty, the recent nuclear deal was a double blow, freeing Iran from sanctions it believed helped check its regional ambitions and raising the specter of better ties between Tehran and Washington, Riyadh’s ally.

While Yemen’s government has long been mired in conflict with Islamist militants, secessionists and tribal fighters, its war coincides with unprecedented turmoil in the Middle East.

Saudi Arabia’s campaign in Yemen marks the first time it has openly confronted what it sees as Iranian regional expansionism.

As long as the war rages in Yemen, there is more space for militants to gain territory as they exploit the security vacuum.

Islamic State and al Qaeda have both emerged in Yemeni regions where they had not previously been present before Saudi Arabia entered the conflict and a Saudi-led coalition began bombing the Houthis in March 2015.

Saudi Arabia and Iran blame each other for Yemen’s conflict, further embittering a regional rivalry between the two nations being played out from Syria to Iraq and Lebanon to Bahrain.

“The situation in the region will probably harden the Saudis’ position against the Houthis - who they view as Iranian proxies,” said April Longley Alley, senior Arabian Peninsula analyst for the International Crisis Group.

In turn, she said, that could empower “more messianic trends within the Houthi movement that see events in the region as the beginning of the end for the Saudi monarchy”.

“EXISTENTIAL NECESSITY” FOR SAUDI

On the battlefield in Yemen the struggle is deadlocked.

Despite Saudi-led air strikes, the Houthis firmly control Sanaa. Hadi’s fighters, backed by mostly Emirati and Saudi forces, have taken control of the now de facto capital - the southern port city of Aden.

A senior diplomat following Yemen said that for the Saudis, the success of the Yemen war was “an existential necessity.”

“From what I see on the ground, the Houthis and Saleh are losing more and more, but there are limits to that. The Houthis are invincible in the north,” he said, adding this means the likelihood that either side will stop fighting is unlikely.

The United States, which backs the U.N.-sponsored peace talks, is a major supplier of weapons to Saudi Arabia and U.S. officials say intelligence-sharing with Riyadh about potential targets in Yemen has been boosted since March.

Coinciding with Saudi Arabia’s cutting ties with Iran, the Saudi-led coalition intensified air strikes on Houthi positions.

Days after the break-off, Tehran accused Saudi Arabia of bombing its embassy in Yemen’s capital of Sanaa, an accusation vigorously denied by Riyadh. Eyewitnesses and residents on the ground also said there was no damage to the embassy.

Pro-Saudi commentators suspected Iran aired the accusation to divert attention from the attack on Riyadh’s embassy in Tehran by protesters enraged at the Shi’ite cleric’s execution.

The clash showed just how quickly rhetoric from the marbled offices in Tehran and Riyadh plays out on the ground in Yemen, stiffening positions among proxies and halting progress in ending a war that has displaced tens of thousands.

Mokhtar al-Rahbi, Hadi’s press secretary, told Reuters the attacks on the Saudi mission had served to harden the views of Sunni Gulf Arab countries, many of whom downgraded their ties in some manner with Iran, against the government in Tehran.

“Iran will find itself solitary, fighting everyone and this will reflect on the Yemen crisis because Iran will now have to give some concessions in Yemen ... in return for some flexibility in the positions of Gulf countries.”

Rahbi also blamed Iran for the failure of the U.N.-brokered peace talks to bear fruit, because the Houthis had “procrastinated” on carrying out key demands.

The latest round of talks in December took place amid a precarious and widely violated truce.

LOW PRIORITY FOR IRAN

Iran’s strategic stake in Yemen is less than in Syria where it is President Bashar al-Assad’s only regional supporter and in Iraq, where it maintains close ideological ties to the Shi’ite-led government.

But Saudi observers are convinced of Iran’s commitment to its allies in Yemen. Many cite remarks by one Iranian official who applauded what he referred to as Iran’s control over four Arab capitals - Beirut, Damascus, Baghdad and Sanaa as proof of what they see as Iran’s dangerous designs on Yemen.

“It is so dangerous for Saudi Arabia, even internally, to accept Iranian hegemony over Yemen or Syria so the price is already high for Saudi Arabia,” said prominent Saudi political commentator Jamal Khashoggi.

Unlike the conflicts in Syria, where Iran has sent fighters from its elite Islamic Revolutionary Guard Corps (IRGC), and in Iraq, where IRGC advisers work alongside Shi’ite Iraqi militias fighting Islamic State, the extent and robustness of Iran’s support to the Houthis is more murky.

But Alley, of ICG, says Iran has made “a very small investment in the Houthis and reaped a large political return”.

“Ironically, the conflict is encouraging the very relationship that Saudi Arabia fears, pushing the Houthis more into the Iranian camp, despite Tehran’s reluctance to get more deeply involved,” Alley said.

Ali Fathollah-Nejad, an Iran expert at the German Council on Foreign Relations, says that while Iran could play a positive role in moderating “perhaps” a few forces in Yemen, its role there had been exaggerated to justify Riyadh’s intervention.

Some speculate that the Yemen war may one day turn into a pawn to be traded in the region’s larger struggle for power.

“To the extent Iran has a strategy in Yemen I suspect they will want Riyadh to concede Syria and Iraq to Iran, in exchange for Iran abandoning its support for the Houthis,” says Karim Sadjadpour, a Senior Associate at the Carnegie Endowment for International Peace.

One Western diplomat involved in regional diplomacy believes resolving the Yemen crisis depends on progress in Syria.

“If there is serious decisive action in Syria -- a political process accompanied by conflict on the ground or vice versa -- Saudi and allies will want to get rid of Yemen more quickly, in order to be able to focus on Syria,” the diplomat said.