The diplomatic crisis surrounding Saudi Arabia and Iran widened on Tuesday as Kuwait recalled its ambassador to Tehran in the face of growing international concern.

Joining Riyadh and its Sunni Arab allies in taking diplomatic action, Kuwait said it was withdrawing its envoy over a weekend attack on the Saudi embassy in Tehran.

Kuwait's move came after the UN Security Council strongly condemned the attack, carried out by protesters angry over Saudi Arabia's execution of a prominent Shiite cleric.

Tensions between Saudi Arabia, the main Sunni power, and Shiite-dominated Iran have erupted this week into a full-blown diplomatic crisis, sparking widespread worries of regional instability.

Iran lashed out again at Saudi Arabia for the execution, with President Hassan Rouhani accusing Riyadh of seeking to "cover its crime" by severing ties. "One does not respond to criticism by cutting off heads," Rouhani said, referring to the usual Saudi practice of carrying out executions with beheading by the sword.

Washington and other Western powers have called for calm amid fears the dispute could raise sectarian tensions across West Asia and derail efforts to resolve conflicts from Syria to Yemen. The Security Council joined those calls late on Monday, issuing a statement urging all sides to "take steps to reduce tensions in the region".

The statement by the 15-member council condemned "in the strongest terms" the attacks which saw protesters firebomb the Saudi embassy in Tehran and its consulate in Iran's second-biggest city Masshad. But the council made no mention of the event that set off the crisis - Saudi Arabia's execution on Saturday of Sheikh Nimr al-Nimr, a cleric and activist whose death sparked widespread protests among Shiites.

Saudi Arabia cut off diplomatic ties with Tehran in protest at the attacks on Sunday and has severed air links with Iran.

Some of its allies among Sunni Arab states followed suit, with Bahrain and Sudan breaking off ties and the United Arab Emirates downgrading relations on Monday.

Kuwait said on Tuesday the embassy attacks "represent a flagrant breach of international agreements and norms and a grave violation of Iran's international commitments". Rouhani has condemned the attacks and Tehran's mission to the UN vowed in a letter to the Security Council to "take necessary measures to prevent the occurrence of similar incidents in the future".