Supporters of Shiite cleric Nimr Baqr al-Nimr, who was executed in Saudi Arabia on Jan. 2, 2015, take part in an anti-Saudi protest in Yemen’s capital, Sanaa, on Jan. 7. (Yahya Arhab/European Pressphoto Agency)

A diplomatic crisis roiling the Middle East intensified Thursday as Iran claimed that a Saudi airstrike overnight hit its embassy in Yemen, a charge not supported by signs of damage but that nevertheless raised tensions between the rivals.

There was no visible evidence of harm to the embassy in Sanaa, the Yemeni capital, which is held by Iranian-friendly rebels who have faced more than nine months of air raids from a Saudi-led military coalition.

But the accusation signaled dangerously heightened friction after Saudi Arabia and a number of fellow Sunni countries severed or downgraded diplomatic relations with Iran, a Shiite-led ­theocracy, over the past week. The row threatened to intensify the rivals’ destructive proxy conflicts in the region, notably in Yemen.

And it cast even more uncertainty over U.S.-backed peace negotiations planned later this month over the civil war in Syria and international efforts to confront the Islamic State militant group.

“Saudi Arabia is responsible for the damage to the embassy building and the injury to some of its staff,” Iranian Foreign Ministry spokesman Hossein Jaber Ansari was quoted as saying by state television news channel IRIB.

1 of 21 Full Screen Autoplay Close Skip Ad × Protests erupt after Saudi Arabia executes Shiite cleric Nimr Baqr al-Nimr View Photos The country’s announcement that it has executed 47 people has caused an uproar across the region. Caption The country’s announcement that it has killed 47 people has caused an uproar across the region. Saudi Arabia severed relations with Iran on Sunday amid the furor. Jan. 3, 2016 A Kashmiri Shiite Muslim, bottom, holds a portrait of Sheikh Nimr Baqr al-Nimr, as others shout slogans during a protest against Saudi Arabia in Srinagar, in India-controlled Kashmir. Mukhtar Khan/AP Buy Photo Wait 1 second to continue.

[Saudi Arabia breaks diplomatic ties with Iran as crisis intensifies]

A spokesman for the Saudi-led military coalition, Ahmed Asseri, promised an investigation into the Iranian accusation, which did not contain specifics.

But, he said by telephone, there is “no proof yet” that coalition airstrikes — which residents of Sanaa say have intensified in recent days — struck the Iranian Embassy or injured any of its staff.

“We will go through all the necessary procedures to see whether this is true or not,” Asseri said, adding that embassies in Sanaa had provided the coalition with coordinates to avoid being struck.

The most recent flare-up between Saudi Arabia and Iran — longtime ideological and strategic rivals whose competition has greatly exacerbated Islam’s Sunni-Shiite rift — began last week: Saudi Arabia executed a prominent Shiite cleric, in response to which protesters in Iran ransacked the Saudi Embassy and a consulate.

Saudi Arabia retaliated Sunday by severing diplomatic relations with Iran, prompting Bahrain, Sudan and Somalia to follow suit. The government in Mogadishu accused Iran of trying to destabilize war-ravaged Somalia. The United Arab Emirates downgraded relations with Iran, while Kuwait and Qatar recalled their ambassadors.

A memorial service for the executed cleric, Nimr Baqr al-Nimr, went ahead peacefully Thursday in Awamiya in Saudi Arabia’s predominantly Shiite eastern region, although armored personnel carriers rumbled through the village and protesters burned tires in the streets, the Associated Press reported.

Saudi Arabia severs ties with Tehran and its diplomats evacuate the Islamic Republic in a worsening diplomatic crisis between the regional rivals. (Reuters)

In Sanaa on Thursday, residents said they saw no evidence of airstrikes against the Iranian Embassy.

A Yemeni security guard said shrapnel from air attacks overnight landed near the compound but fell short of the embassy.

[Brief Yemen truce ends]

The attack took place near the house of a son of Ali Abdullah Saleh, a former Yemeni president whose loyal military units have sided with Yemeni rebels against Saudi-led forces. Saudi Arabia accuses the rebels, Shiites known as Houthis, of being proxies of Iran. Iranian officials deny direct links to the Houthi movement, although they have strongly denounced the Saudi-directed airstrikes and other attacks in ­Yemen.

“Nothing happened here” at the embassy, said the security guard, who spoke on the condition of anonymity because he was not authorized to discuss the subject.

Iran gave no further details on its claim, which was carried by state-run media.

Some officials in Iran and Saudi Arabia have sought to play down the recent tensions, promising that their respective countries will continue to support intensified diplomatic efforts to end the four-year-old Syrian civil war.

Saudi Arabia backs the opposition fighting Syrian President Bashar al-Assad. Bashar’s government, in turn, has received crucial military and economic backing from Iran during fighting that has killed more than 250,000 people and produced an extraordinary refugee crisis.

In comments published Thursday by the Economist, a British magazine, Saudi Arabia’s defense minister ruled out the possibility of war with Iran.

“It is something that we do not foresee at all, and whoever is pushing towards that is somebody who is not in their right mind,” Mohammed bin Salman, who is deputy crown prince, was quoted as saying in an interview conducted this week.

But truculent rhetoric has persisted, punctuating the deep animosity that each side holds for the other.

The deputy leader of Iran’s Revolutionary Guard Corps, Brig. Gen. Hossein Salami, predicted Thursday that flawed policies would cause Saudi Arabia to collapse in the coming years.

“The policies of the Saudi regime will have a domino effect, and they will be buried under the avalanche they have created,” Salami told Iran’s semiofficial Fars News Agency. “If the Saudis do not correct their path, their regime will collapse in coming years.”

Iranian state media also reported Thursday that Iran has banned imports from Saudi Arabia because of the crisis, a move that would affect tens of millions of dollars in annual trade.

Naylor reported from Beirut. Brian Murphy and William Branigin in Washington contributed to this report.

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