TEHRAN — Three Sunni-led countries joined Saudi Arabia on Monday in severing or downgrading diplomatic ties with Iran, worsening a geopolitical conflict with sectarian dimensions in one of the world’s most volatile regions.

The diplomatic protests from the three countries — Bahrain, Sudan and the United Arab Emirates — came as Iran accused Saudi Arabia of using an attack on the Saudi Embassy in Tehran two days earlier as a pretext for diverting attention from its problems.

Iranian protesters ransacked and set fire to the embassy on Saturday, along with the Saudi Consulate in Iran’s second-largest city, Mashhad, after the Saudis executed a Shiite cleric who had criticized the Sunni kingdom’s treatment of its Shiite minority. The Shiite cleric, Sheikh Nimr al-Nimr, was among 47 people who were executed.

The United Nations secretary general, Ban Ki-moon, spoke by phone on Monday with the foreign ministers of Saudi Arabia and Iran, condemning both execution as well as the attack on the embassy. Mr. Ban — who has repeatedly urged the two countries to cooperate on regional conflicts, especially on Syria — called the break in Saudi-Iranian relations “deeply worrying.”