Iranian protesters stormed the Saudi Embassy in Tehran early on Sunday as Shi'ite Muslim Iran reacted with fury to Saudi Arabia's execution of a prominent Shi'ite cleric.

Demonstrators who had massed at the embassy gates to protest against cleric Nimr al-Nimr's execution broke into the embassy and started fires before being cleared away by the police, Iran's ISNA news agency reported.

Pictures posted on Twitter showed parts of the interior on fire and smashed furniture inside one office.

Shortly afterwards, Iran's foreign ministry issued a statement calling for calm and urging protesters to respect the diplomatic premises, the Entekhab news website reported.

Iranian Supreme Leader Ayatollah Ali Khamenei, criticising Saudi Arabia for the second straight day over Nimr's execution, said politicians in the Sunni kingdom would face divine retribution for his death.

"The unjustly spilled blood of this oppressed martyr will no doubt soon show its effect and divine vengeance will befall Saudi politicians," state TV reported Khamenei as saying.

Tehran's police chief, Hossein Sajedinia, told ISNA that an unspecified number of "unruly elements" had been arrested for attacking the embassy with petrol bombs and rocks.

Iran's hardline Revolutionary Guards had promised "harsh revenge" against the Saudi Sunni royal dynasty for Saturday's execution of Nimr, considered a terrorist by Riyadh but hailed in Iran as a champion of the rights of Saudi Arabia's marginalised Shi'ite minority.

Nimr, the most vocal critic of the dynasty among the Shi'ite minority, had come to be seen as a leader of the sect's younger activists, who had tired of the failure of older, more measured leaders to achieve equality with Sunnis.

Although most of the 47 men killed in the kingdom's biggest mass execution for decades were Sunnis convicted of al Qaeda attacks in Saudi Arabia a decade ago, it was Nimr and three other Shi'ites, all accused of involvement in shooting police, who attracted most attention in the region and beyond.

The move appeared to end any hopes that the appearance of a common enemy in the form of the Islamic State militant force would produce some rapprochement between the region's leading Sunni and Shi'ite Muslim powers, who back opposing sides in wars currently raging in Syria and Yemen.

The website of Iran's Supreme Leader, Ayatollah Ali Khamenei, carried a picture of a Saudi executioner next to notorious Islamic State executioner 'Jihadi John', with the caption "Any differences?". The Revolutionary Guards said "harsh revenge" would topple "this pro-terrorist, anti-Islamic regime".

Saudi Arabia summoned the Iranian ambassador, only to see its embassy stormed soon afterwards.

Iraq also furious

In Iraq, whose Shi'ite-led government is close to Iran, prominent religious and political figures demanded that ties with Riyadh be severed, calling into question Saudi attempts to forge a regional alliance against Islamic State, which controls swaths of Iraq and Syria.

Despite the regional focus on Nimr, the executions seemed mostly aimed at discouraging jihadism in Saudi Arabia, where dozens have died in the past year in attacks by Sunni militants.

The ruling Al Saud family has grown increasingly worried in recent years as Middle East turmoil, especially in Syria and Iraq, has boosted Sunni jihadists seeking to bring it down and given room to Iran to spread its influence. A nuclear deal with Iran backed by Saudi Arabia's biggest ally and protector, the United States, has done little to calm nerves in Riyadh.

But Saudi Arabia's Western allies, many of whom supply it with arms, are growing concerned about its new assertiveness in the region and at home.

The US State Department said Nimr's execution "risks exacerbating sectarian tensions at a time when they urgently need to be reduced". The sentiment was echoed almost verbatim by EU foreign policy chief Federica Mogherini and an official at the German Foreign Ministry.

The State Department also urged the Saudi government to "respect and protect human rights, and to ensure fair and transparent judicial proceedings in all cases", as well as to permit peaceful expression of dissent and work with all community leaders to defuse tensions.

The simultaneous execution of 47 people – 45 Saudis, one Egyptian and a man from Chad – was the biggest mass execution for security offences in Saudi Arabia since the 1980 killing of 63 jihadist rebels who seized Mecca's Grand Mosque in 1979.

Anti-government protests

The four Shi'ites had been convicted of involvement in shootings and petrol bomb attacks that killed several police during anti-government protests from 2011-13. More than 20 members of the minority sect were also shot dead by the authorities during those protests.

Family members of the executed Shi'ites have vigorously denied they were involved in attacks and said they were only peaceful protesters against sectarian discrimination.

Human rights groups have consistently attacked the kingdom's judicial process as unfair, pointing to accusations that confessions have been secured under torture and that defendants in court have been denied access to lawyers.

Riyadh denies torture and says its judiciary is independent.

Analysts have speculated that the execution of the four Shi'ites was partly to demonstrate to Saudi Arabia's majority Sunni Muslims that the government did not differentiate between political violence committed by members of the two sects.

The 43 Sunni jihadists executed on Saturday, including several prominent al Qaeda leaders and ideologues, were convicted for attacks on Western compounds, government buildings and diplomatic missions that killed hundreds from 2003-06.

"There is huge popular pressure on the government to punish those people," said Mustafa Alani, a security analyst close to the Saudi Interior Ministry. "It included all the leaders of al Qaeda, all the ones responsible for shedding blood. It sends a message."

Government-appointed clerics have for years denounced al Qaeda and Islamic State as religious "deviants", while the government has cracked down on jihadists at home, squeezed their funding streams abroad and stopped them travelling to fight.

Yet critics say the ruling family has not done enough to tackle the sectarian intolerance, hatred of infidels and praise for the principles of violent jihad propagated by Saudi clerics.

After the executions, Islamic State urged its supporters to attack Saudi soldiers and police in revenge, in a message on Telegram, an encrypted messaging service used by the group's backers, the SITE monitoring group reported.