Iran's president says that Saudi Arabia cannot "cover up" its crime of executing a leading Shia cleric by severing diplomatic relations with the Islamic Republic, even as the kingdom's allies began limiting their links to his country.

President Hassan Rouhani's comments came as Kuwait announced it had recalled its ambassador to Iran over attacks on Saudi diplomatic missions in the Islamic Republic.

The execution last weekend of Sheikh Nimr al-Nimr, a Shia cleric and opposition figure in Saudi Arabia, has heightened the Saudi-Iran regional rivalry, threatening to derail already shaky peace efforts over the wars in Syria and Yemen.

A statement posted on his official website said Rouhani discussed the current diplomatic dispute with visiting Danish Foreign Minister Kristian Jensen.

Hassan Rouhani Iran president

In a statement posted to his website, Iranian President Hassan Rouhani suggested Saudi Arabia 'cannot cover its crime' in executing a Shiite cleric by severing ties with his country. (Beawiharta/Reuters)

"The Saudi government has taken a strange action and cut off its diplomatic relations with the Islamic Republic of Iran to cover its crimes of beheading a religious leader in its country," Rouhani said. "Undoubtedly, such actions can't cover up that big crime."

Addressing journalists Tuesday, Iran's Vice-President Mohammad Bagher Nobakht said the country's intelligence services were investigating the diplomatic mission attacks and that police officers who failed to take action to stop the assaults would be prosecuted. Iranian police say at least 50 people already have been arrested over the attack.

Largest mass execution since 1980

The diplomatic standoff between Iran and the kingdom began Saturday, when Saudi Arabia executed Shia cleric Sheikh Nimr al-Nimr and 46 others convicted of terror charges — the largest mass execution carried out by the kingdom since 1980.

Al-Nimr, a central figure in the Arab Spring-inspired protests by Saudi Arabia's Shia minority, was executed after being convicted of sedition and of other crimes, though he long denied advocating violence.

News of his execution has sparked Shia protests from Bahrain to Pakistan.

In Iran, protesters responded by attacking the Saudi Embassy in Tehran and its consulate in Mashhad. Late Sunday, Saudi Arabia announced it was severing relations with Iran because of the assaults, giving Iranian diplomatic personnel 48 hours to leave.

Sudan and the tiny island kingdom of Bahrain said Monday they would sever ties with Iran The United Arab Emirates announced it would downgrade ties to Tehran to the level of the charge d'affaires, while other nations issued statements criticizing Iran.

Kuwait latest ally to downgrade ties

On Tuesday, Kuwait announced the recalling of its ambassador in a statement carried on the state-run Kuwait News Agency. However, Kuwait did not say it would sever its ties to Iran over the tensions.

Tiny Kuwait is home to both Shias and Sunnis living in peace and has the most free-wheeling political system among all Gulf nations.

Meanwhile Tuesday afternoon, hundreds of Shia protesters marched in Sitra, south of Bahrain's capital, Manama, over al-Nimr's execution. An Associated Press journalist saw police fire tear gas and bird shot, while some protesters threw gasoline bombs. A number of protesters suffered wounds from the birdshot.

Bahrain, a tiny island off the coast of Saudi Arabia, is predominantly Shia, but ruled by Sunnis. It's been the scene of long-running, low-intensity unrest since 2011 Arab Spring-inspired protests.

Iran expressed "regret" over the attacks on the diplomatic missions in a letter to the United Nations on Monday and vowed to arrest those responsible. In the letter, obtained by The Associated Press, Iran's UN envoy Gholamali Khoshroo said more than 40 protesters have been arrested and that authorities are searching for other suspects.

Diplomatic feud escalates3:29

In response to a Saudi letter, the UN Security Council late Monday strongly condemned the attacks by Iranian protesters on Saudi diplomatic posts. The council statement, agreed to after hours of negotiations, made no mention of the Saudi executions or the rupture in Saudi-Iranian relations.

World powers call for calm

Saudi Arabia and Iran have long vied for influence in the Middle East. Their rivalry deepened following the toppling of Saddam Hussein in Iraq and the chaos of the Arab Spring, which gave rise to proxy wars in Syria and Yemen.

World powers have sought to calm the tensions. On Monday, Germany called on both sides to mend ties, while Russian state news agency RIA Novosti quoted an unnamed senior diplomat as saying Moscow is ready to act as a mediator.

The UN envoy for Syria, Staffan de Mistura, was heading to Riyadh, with plans to later visit Tehran. Iran, a staunch supporter of embattled Syrian President Bashar Assad, and Saudi Arabia, a key backer of the opposition, have participated in three rounds of international talks aimed at ending the conflict. De Mistura has set a Jan. 25 target date for a fourth round of talks.

The White House urged Saudi Arabia and Iran to not let their dispute derail efforts to end the Syrian civil war.