Saudi Arabia has given Iranian diplomats 48 hours to leave the country, amid a row over the Saudi execution of a top Shia Muslim cleric.
Saudi Foreign Minister Adel al-Jubeir announced on Sunday the country had broken off diplomatic ties with Iran.
Iran said this would not distract from Riyadh’s “big mistake” in executing the cleric, the IRNA agency reported.
The United States has appealed for calm, saying diplomatic engagement is essential to resolve differences.
Sheikh Nimr al-Nimr and 46 others were executed on Saturday after being convicted of terror-related offences.
Saudi police were shot at late Sunday in his home village, the country’s official SPA news agency said.
Security forces were looking for the attackers, calling the incident a “terrorist” act, SPA reported citing a police spokesman.
Saudi Arabia announced that it would sever diplomatic relations with Iran after demonstrators stormed the Saudi embassy in Tehran.
It has also recalled its diplomats from Tehran.
Mr Jubeir said Saudi Arabia would not let Iran undermine its security, accusing it of having “distributed weapons and planted terrorist cells in the region”.
“Iran’s history is full of negative interference and hostility in Arab issues, and it is always accompanied by destruction,” he told a news conference.
A diplomatic rupture between the major Sunni and Shia powers in the region will resonate across the Middle East where they back opposing sides in many destructive wars and simmering conflicts.
Players are already lining up along sectarian lines to support either Tehran or Riyadh.
Last year had ended with a bit of hope that talks on ending Yemen’s strife had, at least, begun. Syria was to follow this month. It looks an awful lot harder now.
In October Saudi sources told me they only dropped their opposition to Iran’s presence at Syria talks after the US persuaded them to test Tehran’s commitment.
But they doubt Iran will do a deal, and see it as key source of regional instability.
On the other side, Iranian officials don’t hide their contempt for the Saudi system and its support for Islamist groups.
There’s been barely-concealed anger for months. Now it’s boiled over.
US state department spokesman John Kirby said: “We will continue to urge leaders across the region to take affirmative steps to calm tensions”.
“We believe that diplomatic engagement and direct conversations remain essential,” he said.
Earlier, Iran’s Supreme Leader Ayatollah Ali Khamenei warned that the Sunni Muslim kingdom would face “divine revenge” for the execution – an act which also angered Shia Muslims elsewhere in the Middle East.
Ayatollah Khamenei called Sheikh Nimr a “martyr” who had acted peacefully.
Protesters stormed the Saudi embassy in Tehran late on Saturday, setting fire to the building before being driven back by police. The Saudi foreign ministry said none of its diplomats had been harmed in the incident.
Iran is Saudi Arabia’s main regional rival – they back opposing sides in the conflicts in Syria and Yemen.
Relations between the countries have been strained over various issues in recent decades, including Iran’s nuclear programme and deaths of Iranians at the Hajj pilgrimage in 1987 and again in 2015.
Most of the 47 people executed by Saudi Arabia were Sunnis convicted of involvement in al-Qaeda-linked terror attacks over the last decade.
Sheikh Nimr was involved in anti-government protests that erupted in Saudi Arabia in the wake of the Arab Spring, up to his arrest in 2012.
The execution sparked new demonstrations in Saudi Arabia’s Eastern Province, where Shia Muslims complain of marginalisation, as well as in Iraq, Bahrain and several other countries.
The top Shia cleric in Iraq, Ayatollah Ali al-Sistani denounced the execution as an “unjust aggression”.
The leader of Lebanon’s Shia Hezbollah movement, Hassan Nasrallah, launched his sharpest attack yet on the Saudi ruling family on Sunday, accusing them of seeking to ignite a Shia-Sunni civil war across the world.
He said the blood of Sheikh Nimr would “plague the Al Saud [family] until the Day of Resurrection”, prompting cries of “Death to the Al Saud!” among an audience watching his address.
Who was Sheikh Nimr al-Nimr?
In his 50s when he was executed, he has been a persistent critic of Saudi Arabia’s Sunni royal family
Arrested several times over the past decade, alleging he was beaten by Saudi secret police during one detention
Met US officials in 2008, Wikileaks revealed, seeking to distance himself from anti-American and pro-Iranian statements
Said to have a particularly strong following among Saudi Shia youth