Police in Bahrain have fired birdshot and used water cannons to push back demonstrators protesting Saudi Arabia's execution of a Shia cleric.

The protest happened Sunday on Sitra Island, south of Bahrain's capital, Manama. The demonstrators numbered into the hundreds and chanted that Nimr al-Nimr is "our martyr."

Hundreds also marched in al-Daih, west of Manama, chanting slogans against Saudi Arabia's ruling Al Saud family and the Sunni family ruling Bahrain.

These protests followed demonstrations Saturday after Saudi Arabia announced it had executed al-Nimr. Bahrain's Interior Ministry announced Sunday it had arrested "several rioters and vandals ... along with a small number of people who misused social media for illegal purposes" over the protests.

Al-Nimr was an outspoken critic of Saudi Arabia's Sunni monarchy but denied ever calling for violence. His execution has sparked outrage among Shia across the region.

Protesters in Iran

Witnesses say some 400 protesters have gathered at the Saudi Embassy in Tehran after it was stormed overnight.

Authorities had told demonstrators not to protest in front of the embassy and instead gather at a square in central Tehran. The 400 protesters apparently disregarded that, shouting: "Death to Al-Saud!"

Meanwhile, the road the embassy sits on in northern Tehran saw a new street sign come up in recent hours. Instead of saying "Boustan" or "park" in Farsi, it now reads "Sheikh Nimr St." in honour of the Shia cleric.

Tehran authorities could not be immediately reached for comment about the apparent name change for the street.

Protesters have also gathered in Beirut.

'Divine vengeance'

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Iran's supreme leader, Ayatollah Ali Khamenei, said Saudi politicians will face divine retribution for cleric Nimr al-Nimr's death. (Office of the Iranian Supreme Leader/Associated Press)

Iran's President Hassan Rouhani condemned the execution as "inhuman", but also called for prosecuting "extremist individuals" for attacking the embassy and the Saudi consulate in the northeastern city of Mashhad, state media reported.

Iranian Supreme Leader Ayatollah Ali Khamenei, criticizing 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. Iran's 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 marginalized Shia minority.

Nimr was one of 47 men killed in the kingdom's biggest mass execution in decades. Others executed were Sunnis convicted of al-Qaeda attacks in Saudi Arabia a decade ago.

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

"We have received with much sorrow and regret the news of the martyrdom of a number of our brother believers in the region whose pure blood was shed in an unjust aggression," said Iraq's top Shia cleric Grand Ayatollah Ali al-Sistani.

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Protesters demonstrated against the execution of Nimr al-Nimr outside the Saudi Arabian Embassy in London on Saturday. (Neil Hall/Reuters)

The U.S. 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."

UN High Commissioner for Human Rights Zeid Raad al-Hussein said it was not clear those killed were granted effective legal defence, while the scale of the executions was very disturbing "particularly as some of those sentenced to death were accused of non-violent crimes".

Judicial process unfair, say rights groups

Human rights groups say the kingdom's judicial process is 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 Shia 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 al-Qaeda leaders and ideologues, were convicted for attacks that killed hundreds from 2003 to 2006.

"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."

with files from The Associated Press