* More protests planned for Tuesday
* Obama deeply troubled by the violence
By Parisa Hafezi
TEHRAN, June 16 Iranian demonstrators called for more mass protests on Tuesday, a day after hardline Islamic militiamen killed a man during a march by tens of thousands against a presidential election they say was rigged.
The Iranian capital has already seen three days of the biggest and most violent anti-government protests since the 1979 Islamic revolution after hardline incumbent President Mahmoud Ahmadinejad was declared winner of last Friday's vote.
"Tomorrow at 5 p.m. (1230 GMT) at Vali-ye Asr Square," some of the crowd chanted at Monday's march, referring to a major road junction in the sprawling city of some 12 million.
Further protests, especially if they are maintained on the same scale, would be a direct challenge to authorities who have kept a tight grip on dissent since the overthrow of the U.S.-backed shah after months of demonstrations 30 years ago.
U.S. President Barack Obama said on Monday he was "deeply troubled" by post-election violence in Iran.
"The democratic process, free speech, the ability of people to peacefully dissent -- all those are universal values and need to be respected," he told reporters.
The United States and its European allies have been trying to engage Iran and induce the world's fifth-biggest oil exporter to halt nuclear work that could be used to make an atomic bomb. Iran says it only wants nuclear energy to generate electricity.
Obama said he would continue pursuing tough, direct dialogue with Tehran but urged that any Iranian investigation of election irregularities be conducted without bloodshed. The world was inspired by the Iranian protesters, he said.
"WE FIGHT, WE DIE"
Demonstrators filled a broad avenue in central Tehran for several kilometres (miles) on Monday, chanting "We fight, we die, we will not accept this vote rigging", in support of Mirhossein Mousavi, the defeated moderate candidate.
Mousavi said he was "ready to pay any price" in his fight against election irregularities, his Web site quoted him as saying, indicating a determination to keep up the pressure for the election result to be annulled.
Some formed a human chain in front of a building of the Basij Islamic militia, but others broke through and the hardline volunteer paramilitaries opened fire on the crowds sending thousands fleeing in havoc.
One man was killed and many wounded, said an Iranian photographer who witnessed the shooting. Television footage showed one man, his leg covered with blood, being bundled onto the back of a taxi and driven away.
"Tanks and guns have no use any longer," chanted the protesters in a deliberate echo of slogans used leading up to the 1979 revolution.
Members of Iran's security forces have at times fired into the air during the unrest and used batons to beat protesters who have pelted police with stones.
The Basij militia is a volunteer paramilitary force fiercely loyal to Supreme Leader Ayatollah Ali Khamenei who has the final say on all matters of state in Iran.
Gunfire was also heard in three districts of wealthy northern Tehran on Monday evening and residents said there had also been peaceful pro-Mousavi demonstrations in the cities of Rasht, Orumiyeh, Zahedan, and Tabriz on Monday. (Editing by Jon Hemming and Jon Boyle)