* EU says government arguments have "no grounds in reality"
* Thousands pour in to Kiev for fourth anti-Yanukovich rally
* U.S. Senator McCain meets protesters
By Richard Balmforth and Gabriela Baczynska
KIEV, Dec 15 (Reuters) - Thousands massed on Sunday for a rally against President Viktor Yanukovich just days before he heads for a meeting at the Kremlin which the opposition fears will slam the door on integration with the European mainstream.
Minutes before the rally, EU enlargement chief Stefan Fuele said on Twitter he had told Ukraine last week he was suspending work on a trade-and-political agreement, saying Kiev's arguments to improve terms had "no grounds in reality".
Street protests erupted after Yanukovich's decision on Nov. 21 to walk away from the agreement with the EU, after years of careful preparation, and turn to Moscow, Kiev's former Soviet master, for aid to save Ukraine's distressed economy.
Yanukovich's policy swerve, while backed by many in Russian-speaking east Ukraine which is his powerbase, sparked huge disappointment and anger in western and central areas where people see Europe as their proper place.
The weeks-long stand-off between demonstrators in central Kiev and the authorities took on increasing geo-political overtones with the arrival of U.S. Senator John McCain who was due to make a speech at the sprawling protest camp.
Several Western politicians, from Berlin and Brussels, have paid morale-boosting trips to protesters on Independence Square - drawing denunciation from Russian Prime Minister Dmitry Medvedev as "crude" meddling in Ukraine's affairs.
The movement began as a low-level pro-EU protest. But after a police crackdown on a group of mainly students and a face-off between police and protesters last Wednesday, it has broadened into a general outpouring of anger against perceived sleaze and corruption in the country Yanukovich has led for four years.
Protesters characterise it as a battle for Ukraine's soul.
McCain is the latest of a string of European and American dignitaries to tour the sprawling protest camp set up behind barricades of benches, metal barriers, supermarket trollies and wire netting on the square - known locally as the 'maidan'.
"Incredible display of patriotism at the 'Maidan' tonight," McCain tweeted, after meeting Foreign Minister Leonid Kozhara.
McCain later met opposition leaders - the former boxing champion Vitaly Klitchko who leads the UDAR party, former economy minister Arseny Yatsenyuk and far right nationalist Oleh Tyahnybok - and was to speak later Sunday to protesters.
Though Yanukovich has offered up the heads of two minor officials he has shown no sign of meeting the opposition's main request for the dismissal of his prime minister. Talks he had with the opposition on Friday went nowhere.
Yanukovich himself is scheduled to travel to Moscow to meet Russian President Vladimir Putin and tie up agreements to help Ukraine's creaking economy, possibly by securing cheaper prices for gas and credits.
The opposition fears, however, that Yanukovich may be taking the first steps towards joining a Moscow-led customs union, together with Belarus and Kazakhstan - which they see as an attempt by Putin to re-create the Soviet Union.
Klitschko's UDAR party called on Sunday for the dismissal of Andriy Kluyev, one of Yanukovich's closest security aides, whom the opposition says was behind past attempts to break up the protests by force.
SMOKE, ROCK AND LASER
Smoke rose from scores of wood-burning braziers where protesters crouched for warmth on Independence Square on Saturday night. A popular Ukrainian rock band, Okean Elzy, belted out numbers while green laser lighting streaked across the sky to spell out 'Ukraine loves the EU' on the side of the cavernous Soviet-era post office.
Thousands, their bedrolls over the shoulders, shuffled onto the square, squeezing their way through a tight human channel of security committee officials checking for possible 'provocateurs'.
"I heard he (McCain) was here. It's nice that they know of us, that they remember us. It is great that they support us," said Volodimir Tarabanov, 28, who works for a delivery company in Kiev.
Crowds sang the Ukrainian national anthem repeatedly throughout the night and chanted "Glory to Ukraine!, Glory to Heroes!". As dawn broke on the square, priests intoned prayers to the protesters from a huge screen hanging over the square.
Apart from those on the 'Euro-Maidan', thousands of Yanukovich supporters staged a rival rally in Kiev on Saturday, many bussed in from Donetsk and other cities in eastern Ukraine.