* Some demonstrators chant "Long live Reza Shah", breaking a taboo
* Iranians protest against government and religious establishment
* Frustrations with economic hardships and alleged corruption
LONDON, Dec 31 (Reuters) - Iran warned of a crackdown on Sunday against demonstrators who pose one of the biggest challenges to both the government and clerical leadership in power since the 1979 revolution.
Tens of thousands of Iranians have protested across the country since Thursday against the Islamic Republic's unelected clerical elite and Iranian foreign policy in the region. They have also chanted slogans in support of political prisoners.
Demonstrators initially vented their anger over economic hardships and alleged corruption but they have also begun to call on Supreme Leader Ayatollah Ali Khamenei to step down.
Videos posted on social media showed people chanting: "Mullahs, have some shame, leave the country alone."
The demonstrators also shouted: "Long live Reza Shah". Such calls are evidence of an unprecedented level of anger and break a taboo. The king ruled Iran from 1925 to 1941 and his Pahlavi dynasty was overthrown in a revolution in 1979 by Ayatollah Ruhollah Khomeini, the Islamic Republic's first leader.
The protests are the biggest since unrest in 2009 that followed the disputed re-election of then-President Mahmoud Ahmadinejad.
They are also troublesome for the government of President Hassan Rouhani because he was elected on a promise to guarantee rights to freedom of expression and assembly.
Rouhani's main achievement is a deal in 2015 with world powers that curbed Iran's nuclear program in return for a lifting of most international sanctions. But it is yet to bring the economic benefits the government promised.
"Those who damage public property, violate law and order and create unrest are responsible for their actions and should pay the price," state media quoted Interior Minister Abdolreza Rahmani Fazli as saying.
PROTESTS APPEAR SPONTANEOUS
Protesters defied the police and Revolutionary Guards who have used violence to crush previous unrest. The demonstrations could be more worrying for authorities because they seem spontaneous and lack a clear leader.
No political party has urged Iranians to take to the streets and opposition leaders who galvanised Iranians during 2009 are under house arrest. In addition, the range of slogans suggests discontent across social classes with government policies.
Iran has a dual system of clerical and republican rule, in which each faction vies for control. The supreme leader rules for life and is commander-in-chief of the armed forces. He also appoints the head of the judiciary and, in all, has more power over foreign and economic policy than the elected president.
In apparent response to the protests, the government backed down on plans to raise fuel prices, promised to increase cash handouts to the poor and create more jobs in coming years.
"We predict that at least 830,000 jobs will be created in the new year," government spokesman Mohammad Baqer Nobakht said on state television on Saturday night. He gave no details. Around 3.2 million Iranians are jobless.
Iranians also expressed anger over their country's costly interventions in Syria and Iraq where it is engaged in a proxy war for influence against regional rival Saudi Arabia.
Videos on social media showed protesters in the city of Shiraz tearing down a banner of Qassem Soleimani, the powerful head of the Quds Force, the branch of the Iranian Revolutionary Guards' that overseas operations in Iraq, Syria and elsewhere.
"The time has come for the regime in Iran to end terrorist activities, corruption & their disregard for human rights," said U.S. Vice President Mike Pence on his Twitter page.
Protesters have attacked banks and government buildings and burned police vehicles. Two demonstrators were shot dead in the western town of Dorud on Saturday night. The deputy governor of Lorestan province blamed foreign agents for the deaths.
"No shots were fired by the police and security forces. We have found evidence of enemies of the revolution, Takfiri groups and foreign agents in this clash," Habibollah Khojastehpour said in an interview on state television on Sunday. Takfiri is a term for extreme Sunni militants such as Islamic State.
Ahmad Khatami, a hardline cleric who leads Friday prayers in the capital Tehran, said the protests were similar to those in 2009 over alleged electoral fraud.
He called for capital punishment for those chanting slogans against the values of the Islamic Republic. (Writing by Michael Georgy; Editing by Matthew Mpoke Bigg)