(Adds footage showing protests for fourth day)
* Students keep up pressure of daily protests
* Military took days to admit plane shot down
* Tension built up since U.S. quit nuclear pact
* European powers trigger pact dispute mechanism
By Parisa Hafezi and Babak Dehghanpisheh
DUBAI, Jan 14 (Reuters) - Iran said on Tuesday it had arrested people accused of a role in shooting down a Ukrainian airliner and had also detained 30 people involved in protests that have swept the nation for four days since the military belatedly admitted its error.
Wednesday's shooting down of Ukraine International Airlines flight 752, killing all 176 people aboard, has led to one of the biggest public challenges to the Islamic Republic's clerical rulers since they took power four decades ago.
In a step that will increase diplomatic pressure, Britain, France and Germany launched a dispute mechanism to challenge Iran for breaching limits on its nuclear programme under an agreement which Washington abandoned in 2018.
Since the United States killed Iran's most powerful military commander in a drone strike on Jan. 3, Tehran has faced escalating confrontation with the West and unrest at home, both reaching levels with little precedent in its modern history.
Iran shot down the airliner on Wednesday when its military was on high alert, hours after it had fired missiles at U.S. targets in Iraq. After days of denying a role in the air crash, it admitted it on Saturday, calling it a tragic mistake.
Protesters, many of them students, have held daily demonstrations since then, chanting "Clerics get lost!" and calling for the removal of Supreme Leader Ayatollah Ali Khamenei, in power for more than 30 years.
Police have responded to some protests with a violent crackdown, video posts on social media showed. Footage showed police beating protesters with batons, wounded people being carried, pools of blood on the streets and the sound of gunfire.
Iran's police denied firing at protesters. The judiciary said 30 people had been detained in the unrest but said the authorities would show tolerance towards "legal protests".
'WHERE IS JUSTICE?'
Video posts on Tuesday showed scores gathered peacefully at two Tehran universities. "Where is justice?" one group chanted.
The extent of the unrest is difficult to assess because of limits on independent reporting. Demonstrations tend to gather momentum later in the day and clashes have been at night.
President Hassan Rouhani promised a thorough investigation into the "unforgivable error" of shooting down the plane. He spoke in a television address on Tuesday, the latest in a series of apologies from a leadership that rarely admits mistakes.
Judiciary spokesman Gholamhossein Esmaili said some of those accused of having a role in the plane disaster had been arrested, although he did not say how many or identify them.
Most of those on board the flight were Iranians or dual nationals. Canada, Ukraine, Britain and other nations who had citizens on the plane have scheduled a meeting on Thursday in London to consider legal action against Tehran.
The disaster and subsequent unrest comes amid one of the biggest escalations between Tehran and Washington since 1979.
Missiles launched at a U.S. base in Iraq killed an American contractor in December, an attack Washington blamed on an Iran-backed group. Confrontation eventually led to the U.S. drone strike on Jan. 3 that killed Qassem Soleimani, architect of Iran's regional network of proxy militias.
Iran's government was already reeling from the reimposition of sanctions by the United States, which quit an agreement with world powers under which Tehran would secure sanctions relief in return for scaling back its nuclear programme.
Since Washington withdrew, Tehran has stepped back from its nuclear commitments and has said it would no longer recognise limits on enriching uranium. After months of threatening to act, European signatories to the deal, France, Britain and Germany, activated the agreement's dispute mechanism on Tuesday.
The European Union's top diplomat said the European move aimed to bring Tehran bank to compliance, not impose sanctions.
Iran's leaders have been facing a powerful combination of pressure both at home and abroad.
Just two months ago, Iran's authorities put down anti-government protests, killing hundreds of demonstrators in what is believed to be the most violent crackdown on unrest since the 1979 revolution.
Elsewhere in the Middle East, where Iran has wielded influence through a network of allied movements and proxies, governments that include powerful Iran-sponsored armed factions have faced months of hostile demonstrations in Lebanon and Iraq.
Iran's president said in his address that those responsible for shooting down the plane would be punished, describing the military's admission of its mistake "a good first step."
Rouhani also said the government would be accountable to Iranians and those nations who lost citizens. Iranian state television said aviation officials from Canada, which had 57 citizens on the doomed flight, as well as from Iran and Ukraine, met in Tehran on Tuesday to discuss the investigation.
(Reporting by Parisa Hafezi and Babak Dehghanpisheh and John Irish in Paris Writing by Edmund Blair Editing by Peter Graff)
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