Saudi Arabia accused Iran of sponsoring terror and undermining regional stability, as a diplomatic spat between both countries escalated Saturday over the kingdom's execution of a prominent Shia cleric.

"The Iranian regime is the last regime in the world that could accuse others of supporting terrorism, considering that (Iran) is a state that sponsors terror, and is condemned by the United Nations and many countries," said a foreign ministry spokesman in a statement carried by the official SPA news agency.

The statement was the second after the kingdom's foreign ministry announced it had summoned the Iranian ambassador in Riyadh to protest an "aggressive" statement by Tehran on the execution of Saudi Shia cleric Nimr al-Nimr.

"Iran's regime has no shame as it rants on human rights matters, even after it executed hundreds of Iranians last year without a clear legal basis," said the statement.

In Tehran meanwhile, angry crowds hurled Molotov cocktails and stormed the Saudi embassy in protest at Nimr's execution before being cleared by police, ISNA news agency reported. Fires were seen burning inside the building, it said.

Nimr, who spent more than a decade studying theology in Iran and had been a driving force behind Shia-led anti-government protests in Saudi Arabia since 2011, was among a group of 47 Shias and Sunnis executed Saturday for "terrorism".

The group included many Qaeda-linked militants involved in deadly bombings in the kingdom since 2003.

Shia-dominated Iran, the Sunni kingdom's longtime foe, said in reaction to Nimr's execution that "the Saudi government supports terrorist movements and extremists, but confronts domestic critics with oppression and execution."

It will "pay a high price for following these policies," said Iran's foreign ministry spokesman Hossein Jaber Ansari.

Iran's statements reveal its "true face as a backer of terrorism, which is a continuity of its policies in undermining security and stability in the region," the unidentified Saudi ministry spokesman said.

"By defending the acts of terrorists... the Iranian regime is considered a partner in their crimes and is held completely responsible for its policies of incitement and escalation."

Iran has offered "many Al-Qaeda leaderships safe haven since 2001" in addition to "offering an Iranian passport" to a Saudi suspect involved in 1996 bombings in the kingdom who was arrested last year, the ministry said.

It criticised Iran's "flagrant interferences in regional countries, including Iraq, Yemen, and Lebanon, as well as Syria where it has directly intervened through its Revolutionary Guard and Shia militia" causing the death of tens of thousands of Syrians.

Iran-linked cells smuggling explosives and arms to Bahrain and Kuwait have also been uncovered, the kingdom recalled.

Regional heavyweights Saudi Arabia and Iran are supporting opposite sides in several conflict zones across the region.

Saudi Arabia's "justice system is independent, just and transparent and does not... operate discreetly as the case in Iran," the statement added.