(Adds Putin Obama, updates toll, edits)
* Protesters force riot police from Kiev square, capture policemen
* At least 39 more dead as violence forces EU talks venue change
* EU offers political roadmap, Russia slams "doormat"
* Interior minister says police given combat arms, will use them
By Richard Balmforth and Alessandra Prentice
KIEV, Feb 20 (Reuters) - Ukraine suffered its bloodiest day since Soviet times on Thursday with a gun battle in central Kiev as President Viktor Yanukovich faced conflicting pressures from visiting European Union ministers and his Russian paymasters.
Three hours of fierce fighting in Independence Square, which was recaptured by anti-government protesters, left the bodies of over 20 civilians strewn on the ground, a few hundred metres from where the president met the EU delegation.
The ministers, from Germany, France and Poland, shuttled through "a night of difficult negotiations" with him and the opposition, said EU officials who hoped a plan for an interim government and early elections could bring peace.
Earlier in the day, riot police were captured on video shooting from a rooftop at demonstrators in the plaza, known as the Maidan. Protesters hurled petrol bombs and paving stones to drive the security forces off a corner of the square the police had captured in battles that began two days earlier.
The health ministry said 75 people had been killed since Tuesday afternoon, which meant at least 47 died in Thursday's clashes. That was by far the worst violence since Ukraine emerged from the crumbling Soviet Union 22 years ago.
The trio of EU foreign ministers met for a marathon four hours with Yanukovich and extended their stay until Friday to put a roadmap for a political solution to opposition leaders after colleagues in Brussels imposed some targeted sanctions and threatened more if the authorities failed to restore calm.
Vitaly Klitschko, an opposition leader, said he hoped for a deal overnight but added there was no clear result so far.
In global diplomacy at the highest level, U.S. President Barack Obama spoke to German Chancellor Angela Merkel who in turn discussed Ukraine with Russian President Vladimir Putin.
Putin "stressed the critical importance of an immediate end to bloodshed, the need to take urgent measures to stabilise the situation and suppress extremist and terrorist attacks" the Kremlin said - sharing Yanukovich's view that he faces a coup.
The White House said Obama and Merkel agreed it was "critical" U.S. and EU leaders "stay in close touch in the days ahead on steps we can take to support an end to the violence and a political solution that is in the best interests of the Ukrainian people". Earlier this month, bugged and leaked diplomatic phone calls exposed EU-U.S. disagreement on Ukraine.
The EU plan "offers a chance to bring an end to violence," Polish Prime Minister Donald Tusk said in Warsaw, adding that Yanukovich was willing to hold rapid elections to parliament and the presidency - the latter something Yanukovich has so far appeared reluctant to consider, a year before his term ends.
"Progress made but important differences remain," Polish Foreign Minister Radoslaw Sikorski tweeted from Kiev as demonstrators on Independence Square held a vigil after dark for fallen comrades, lit by mobile phone screens held aloft.
Medics carried bodies on stretchers through lines of protesters who chanted "Heroes, heroes" to the dead.
Though armed militants on the barricades tend to be from the far-right fringe, the opposition has broad support. But many Ukrainians also fear violence slipping out of control:
"This is brother fighting brother," said Irina, a local woman walking to Independence Square to donate syringes for blood transfusions. "We need to realise we're all one people."
In a sign of faltering support for Yanukovich, his hand-picked head of Kiev's city administration quit the ruling party in protest at bloodshed in the streets.
But core loyalists were still talking tough.
Interior Minister Vitaly Zakharchenko, wearing camouflage as he made a televised statement, said police had been issued with combat weapons and would use them "in accordance with the law" to defend themselves - or to free 67 of their colleagues his ministry said were being held captive.
Demonstrators said captured police had been allowed to go.
Russia criticised European Union and U.S. actions, calling them "blackmail" that would only make matters worse. Putin dispatched an envoy to Kiev to join the mediation effort.
Ukraine is caught in a geopolitical tug-of-war between Moscow - which sees it as a market and ally and fears protests spreading to Russia - and the West, which says Ukrainians should be free to choose economic integration with the EU.
Raising pressure on Yanukovich to restore order if he wants another desperately needed loan, Russian Prime Minister Dmitry Medvedev said Moscow would not hand over cash to a leadership that let opponents walk over it "like a doormat".
Thursday morning's bloodshed, in which both sides used firearms, traumatised many Ukrainians, whose 2004-05 Orange Revolution for democracy passed off largely peacefully.
It heightened concern voiced by Tusk earlier this week that Ukraine could descend into civil war or split between the pro-European west and Russian-speaking east.
Video of the clashes on the edge of the Kiev square showed "Berkut" riot policemen firing bursts from automatic rifles on the run as they covered retreating colleagues fleeing the plaza. One policeman used a sniper rifle. An opposition militant in a helmet was filmed firing from behind a tree.
Other protesters used police riot shields for cover, while some fell wounded as the protest camp became a killing zone. A presidential statement said dozens of police were wounded or killed during the opposition offensive, hours after Yanukovich and opposition leaders had agreed on a truce.
The interior ministry's website advised citizens to avoid central Kiev because of the danger from "armed and aggressive individuals". Schools, restaurants and many shops in the normally bustling city of 3 million were closed, the metro was shut down and bank machines were running out of cash.
A statement from Yanukovich's office said organised gangs of protesters were using firearms, including sniper rifles.
"COLD WAR CHESSBOARD"
Wounded protesters were given first-aid treatment in the lobby of the Ukraine Hotel, where many foreign correspondents are staying. Reporters said there were bullet holes in the walls and windows of the hotel overlooking the square.
The crisis in the sprawling country of 46 million with an ailing economy and endemic corruption has mounted since Yanukovich took a $15-billion Russian bailout instead of signing a wide-ranging trade and cooperation deal with the EU.
Russia has held back a new loan instalment until it sees stability in Kiev and has condemned EU and U.S. support of the opposition demands that Yanukovich, elected in a broadly fair vote in 2010, should share power and hold new elections.
Obama has rejected suggestions Ukraine is a pawn in a global confrontation with Moscow: "Our approach in the United States is not to see these as some Cold War chessboard in which we're in competition with Russia," he said on Wednesday.
At Russia's Winter Olympics in Sochi, a Ukrainian skier pulled out in solidarity with "friends at the Maidan" because of the violence back home and Ukrainian team officials and competitors held a minute's silence for the dead.
In Lviv, a bastion of Ukrainian nationalism since Soviet times, the regional assembly declared autonomy from Yanukovich and his administration, which many west Ukrainians see as much closer to Moscow and to Ukraine's Russian-speaking east.
Ukraine's hryvnia currency, flirting with its lowest levels since the global financial crisis five years ago, weakened again on Thursday. Ukraine's state debt insurance costs rose to their highest since December 2009.
Possibly from fear of sanctions, some of Ukraine's richest magnates have stepped up pressure on Yanukovich to hold back on using force: "There are no circumstances which justify the use of force toward the peaceful population," said "oligarch" Rinat Akhmetov, who bankrolled Yanukovich's 2010 election campaign. (Additional reporting by Natalya Zinets, Pavel Polityuk, Vasily Fedosenko and Sabine Siebold in Kiev, John Irish in Paris and Francesco Guarascio and Adrian Croft in Brussels; Writing by Richard Balmforth and Paul Taylor; Editing by Alastair Macdonald)