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 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 erupted this week into a full-blown diplomatic crisis sparking widespread worries of regional instability.

Iran on Tuesday lashed out again at Saudi Arabia over Saturday's 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 the Middle East 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 Mashhad.

But the council made no mention of the event that set off the crisis -- Saudi Arabia's execution of Sheikh Nimr al-Nimr a cleric and activist whose death sparked widespread Shiite protests.

- 'Grave violation' -

Riyadh cut 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.

Bahrain -- base of the US Fifth Fleet -- cut air links with Iran on Tuesday.

Kuwait said 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".

Iranian officials have brushed aside the dispute with government spokesman Mohammad Bagher Nobakht saying Tuesday it "will have no impact on Iran's national development".

"It is Saudi Arabia that will suffer" he said.

US Secretary of State John Kerry called his Iranian and Saudi counterparts on Monday to urge calm as European leaders voiced concerns and Moscow offered to mediate.

UN Secretary General Ban Ki-moon also spoke by phone with the Saudi and Iranian foreign ministers to urge them to "avoid any actions that could further exacerbate the situation" his spokesman Stephane Dujarric said.

"A breakdown of relations between Riyadh and Tehran could have very serious consequences for the region" Dujarric said.

The UN envoy for Syria Staffan de Mistura rushed to Riyadh in a bid to defuse tensions. He is also expected in Iran later this week and in Damascus on Saturday UN sources said.

- Regional rivals -

The official Saudi SPA news agency without referring to the Iran crisis said Foreign Minister Adel al-Jubeir reaffirmed to the envoy Tuesday Riyadh's view that "(President) Bashar al-Assad doesn't have any role in Syria's future".

The UN quoted De Mistura as saying Riyadh was determined that regional tensions "will not have any negative impact... on the continuation of the political process that the UN together with the International Syria Support Group intend to start in Geneva soon".

And the Security Council called for a new ceasefire in Yemen and a return to peace talks despite the Saudi-Iran crisis.

The six-nation Gulf Cooperation Council (GCC) of Sunni Arab states said it would meet in Riyadh Saturday for talks on the embassy attacks a day before an Arab League emergency meeting.

The foreign minister of Shiite-majority Iraq was due in Tehran Wednesday Iran state media reported "in the framework of improving Iran-Iraq bilateral relations".

Media reports said his counterpart from Oman which has often played the role of mediator in the region was also expected in the Iranian capital.

Iran and Saudi Arabia are on opposing ends of a range of crucial issues including the war in Syria -- where Tehran backs Assad's regime and Riyadh supports rebel forces -- and Yemen where a Saudi-led coalition is battling Shiite insurgents.

The spike in tensions comes after Iran last year secured a historic nuclear deal with world powers led by the United States sparking major concern in longtime US ally Riyadh.

Nimr one of 47 men executed on Saturday was a driving force behind 2011 anti-government protests in Saudi Arabia's Eastern Province.

He was arrested in 2012 after calling for two Saudi governorates to be separated from the kingdom.

More trouble flared in Eastern Province Tuesday when gunmen intercepted and torched a bus without causing casualties two days after a civilian was shot dead in Nimr's home village.