Iran is accusing Saudi warplanes of bombing its embassy in Sanaa, the Yemeni capital, as already-heightened tensions between the two most-powerful Muslim countries in the Middle East continues to rise.

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

Reuters quoted Brigadier-General Ahmed Asseri, a spokesman for the Saudi-led coalition in Yemen, as saying the Iranian allegation will be investigated.

The two countries are involved on opposite sides of the Yemeni civil war. The Saudi-led coalition of mostly Sunni Muslim countries supports the government of President Abdu Rabbu Mansour Hadi, who was driven from power by the Houthi rebels and is now in exile. Iran, which is Shia, supports the Houthi rebels, who adhere to a strain of Shia Islam. Although the rivalry between Saudi Arabia and Iran is often portrayed as part of the 1,400-year-old schism in Islam, the Sunni-Shiite divide doesn’t quite explain it. (You can read my colleague Uri Friedman’s piece about it here, and also David Graham’s stories on Saudi Arabia, Iran, and their respective Shia and Sunni minorities here.)

Besides being on opposite sides of the civil war in Yemen, Saudi Arabia and Iran are also jostling for influence across the broader Middle East: In Syria, Riyadh supports some rebel groups and Iran the government of President Bashar al-Assad; in Bahrain, a Saudi-backed Sunni ruler governs a mostly Shia population, some of whom look to Iran; and in Iraq, Iran holds considerable influence over the predominantly Shia government. The two countries have also traded barbs over the death toll of the stampede at the Hajj last September.

But such tensions, which have been simmering since the creation of the Islamic Revolution in 1979, increased sharply last weekend when Saudi Arabia executed Sheikh Nimr al-Nimr, a Shia cleric, and 46 others, mostly Sunni, on charges of terrorism. The execution prompted disapproval from Washington and other Western capitals, but they provoked outrage in Iran and other cities around the world with considerable Shia populations. The Saudi Embassy in Tehran was attacked and set on fire, and the consulate in Mashhad was also attacked. In response, Saudi Arabia severed diplomatic relations with Iran, and many of its allies either followed suit, recalled their envoys, or downgraded ties with Tehran.

The deterioration of relations between the two most powerful Muslim countries in the Middle East complicates efforts to negotiate a settlement to the Syrian civil war. In Syria, the U.S. and its allies are trying to cobble together an international coalition to fight ISIS. Both Iran and Saudi Arabia say they oppose the group, but given the current tensions they could draw closer to their clients—Assad for Iran; the rebels for the Saudis—in that conflict. Also, according to The New York Times, the tensions threaten progress against ISIS in neighboring Iraq.