* New opposition Coordination Council under attack
* Holds first session, agrees on next anti-Kremlin rally in Dec
* Kremlin-friendly billionaire launches political party
By Maria Tsvetkova and Gleb Bryanski
MOSCOW, Oct 27 (Reuters) - Three prominent opponents of Russian President Vladimir Putin were briefly detained at a protest in central Moscow on Saturday that followed the first meeting of a new opposition body elected in an online vote.
Police arrested politicians Alexei Navalny, Ilya Yashin and Sergei Udaltsov as they tried to take part in a march of several dozen opposition supporters after the inaugural session of the newly-formed Coordination Council.
The opposition group, which met in a Moscow cafe, is tasked with trying to mount a structured challenge to Putin, who assumed the presidency in May for a six-year term.
"They gave us the mandate of trust and made us responsible for coordinating efforts of dozens, hundreds, thousands and millions of people who want positive changes in our country," said Navalny, a popular blogger who collected most of the votes.
While Putin has faced spirited dissent since returning to the presidency for his third term, his critics have so far failed to make significant inroads into his grip on power.
More than 81,000 people took part in the vote, underscoring the scale of the challenge the opposition faces in a country with a population of 142 million people.
After some bickering on Saturday, the new group of 45 leaders agreed to hold the next rally in December to mark the anniversary of the first anti-Putin protests.
Opposition supporters shouted "Shame!" as police ushered Navalny, Yashin and Udaltsov into police vans. The three were released after several hours at the police station and face fines of up to 30,000 roubles (about $1,000) or up to 50 hours of community work for violating public order.
Their arrests followed the detention this month of activist Leonid Razvozzhayev who said he was abducted in Ukraine and tortured.
Kremlin critics in Russia and abroad say the detentions signal a crackdown on dissent since Putin started his new term.
"Reports about new arrests of democratic opposition activists in Moscow. Many signs points at a much harsher regime attitude," Swedish Foreign Minister Carl Bildt wrote in his Twitter microblog.
The Kremlin, which has so far ignored the opposition vote, poured scorn on the Council's first session saying that the new leaders were not capable of proposing a constructive agenda or moving the country forward.
"The fact that the opposition is debating how to mark the anniversary of its protests shows that they are looking into the past, not the future," Interfax quoted Aleksei Chesnakov, one of the leaders of pro-Kremlin party United Russia, as saying.
Sergei Mironov, leader of left-leaning Just Russia party which holds 64 seats in the parliament, threatened to expel two of his party members who were elected in the Council and said anti-Kremlin protesters were turning into a sect.
Communist leader Gennady Zyuganov told his party congress that he had warned leftist Udaltsov against siding with "liberals" like Navalny and Yashin who dominate the Council.
Police said the three activists arrested on Saturday were detained for public order violations. It said the protest was not sanctioned by Moscow authorities, as required by law.
While pro-Kremlin television channels barely mentioned the Coordinating Council meeting, they gave plenty of air time to the launch of billionaire Mikhail Prokhorov's new party Civil Platform which pledged to pursue a liberal economic agenda.
Prokhorov, a tycoon whose fortune is estimated by Forbes magazine at $13 billion, said he will now hand over the management of his business assets to partners and focus on politics.
The businessman challenged Putin in the March election, but critics said he had been picked by the Kremlin as a token opposition figure. He collected almost 8 percent of the vote.
"From this day I will only engage in political activity and nothing else," Prokhorov told his supporters. "There is an opinion that here one can either be with the Kremlin or with the Coordination Council. This is not true."