* Pro-government rallies commemorate end of 2009 unrest
* Anti-government protests spurred by hardships resume
* Tehran students stone police, pro-gov't crowd forms nearby
* Online videos show police clubbing, arresting protesters
* Trump criticises arrests, Iran rejects criticism (Adds security forces intervene to disperse protesters)
DUBAI, Dec 30 (Reuters) - Anti-government protests broke out in Iran for the third day running on Saturday as separate state-sponsored rallies were staged to mark the end of unrest that shook the country in 2009, according to Iranian news agencies and state media.
State television showed a rally in the capital Tehran as well as marchers carrying banners in support of Supreme Leader Ayatollah Ali Khamenei in Mashhad, Iran's second largest city where protests over prices turned political on Thursday.
State-sponsored mass rallies were scheduled in more than 1,200 cities and towns, state TV said - events held annually to commemorate the end of months of street protests that followed Mahmoud Ahmadinejad's disputed re-election as president.
At the same time, social media postings said protests broke out for the third straight day in cities including Tehran and Kermanshah. One video showed dozens of protesters booing after police announced by loudspeaker that any gathering would be illegal. The footage could not be authenticated.
The semi-official news agency Fars said up to 70 students gathered in front of Tehran University and hurled rocks at police. A social media video showed them chanting "Death to the dictator", an apparent reference to Khamenei.
Footage later showed riot police clubbing and arresting the protesters. ISNA news agency said a group of government supporters also gathered outside the university as police tried to disperse protesters. Authorities closed two nearby metro stations "until the end of the unrest", ISNA said.
Another video appeared to show security forces arresting demonstrators in another part of Tehran, with protesters shouting "Let him go! Let him go!"
In a further video, which could not be verified, marchers in the western town of Dorud chanted, "Death to the dictator".
Dozens of protesters gathered in the western city of Shahr-e Kord, ISNA said. Social media footage appeared to show a protester being helped by his comrades after being teargassed.
Openly political protests are rare in the Islamic Republic, where security services are omnipresent.
But there is considerable discontent over high unemployment, inflation and alleged graft. Some of the new protests have turned political over issues including Iran's costly involvement in regional conflicts such as those in Syria and Iraq.
Joblessness has risen and annual inflation is running at about 8 percent, with shortages of some foods contributing to higher prices and hardship for many families.
Interior Minister Abdolreza Rahmani-Fazli warned against attempts to promote protests via social media.
"We ask people not to take part in unlawful gatherings. If they plan a gathering they should apply (for a permit," he told the Young Journalists Club news website.
On Thursday, hundreds of people took to the streets in Mashhad, one of the holiest places in Shi'ite Islam, to protest against high prices and shouted anti-government slogans. Police arrested 52 people, according to a judicial official.
The United States condemned the arrests, with President Donald Trump tweeting: "Iranian govt should respect their peoples rights, including right to express themselves. The world is watching!"
State media quoted Foreign Ministry Spokesman Bahram Qassemi as saying in response: "The Iranian people see no value in the opportunistic claims by American officials and Mr. Trump."
Friday witnessed the largest wave of demonstrations since 2009 as protests spread to Tehran and other cities.
State broadcaster IRIB had not covered the protests "after being asked by relevant bodies that the issue should not be reflected on state radio and television", its website quoted an unnamed official as saying.
MOST DETAINEES FREED
Most of those arrested in the last two days had been released, state TV said, without giving details.
"Enemy websites and foreign media continue to try to exploit economic hardships and the legitimate demands of the people in this respect to launch illegal gatherings and possible unrest," it said.
The elite Revolutionary Guards and its Basij militia, which spearheaded the security crackdown that crushed the protests of 2009, said in a statement carried by state media: "The Iranian nation ... will not allow the country to be hurt."
Though purely political protests are seldom seen in Iran, demonstrations are often held by workers over lay-offs or non-payment of salaries and by people who hold deposits in non-regulated, bankrupt financial institutions.
President Hassan Rouhanis leading achievement, a 2015 deal with world powers that curbed Irans nuclear program in return for a lifting of most international sanctions, has yet to bring the broad economic benefits the government says are coming.
Unemployment has risen to 12.4 percent this fiscal year, according to the Statistical Centre of Iran, up 1.4 percentage points and leaving about 3.2 million Iranians jobless. (Reporting by Dubai newsroom; editing by Mark Heinrich)