* Thousands pour into Kiev for fourth anti-Yanukovich rally
* EU suspends work on trade deal with Ukraine
* U.S. Senator McCain: "Your destiny is with Europe"
By Richard Balmforth and Alissa de Carbonnel
KIEV, Dec 15 (Reuters) - Thousands massed on Sunday for a rally against Ukrainian President Viktor Yanukovich just days before he heads for a meeting in 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 he was suspending work on a trade and political deal, saying Kiev's arguments to improve terms had "no grounds in reality".
Fuele's words suggested the European Union has lost patience with demands for financial aid from Kiev and with the part the bloc was being forced to play in a 'bidding war' with Russia over Ukraine.
But U.S. Senator John McCain galvanised the 200,000 or so people on Kiev's Independence Square, telling them their destiny lay in Europe.
"We are here to support your just cause, the sovereign right of Ukraine to determine its own destiny freely and independently. And the destiny you seek lies in Europe," said McCain, a leading Republican voice on U.S. foreign policy.
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 Soviet-era overlord, 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 presence of McCain at the anti-government rally after a weeks-long stand-off between demonstrators and the authorities further highlighted the geo-political East-West tug-of-war which Ukraine is once again at the centre of.
Western politicians, from Berlin and Brussels, have paid morale-boosting trips to the square drawing denunciation from Russian Prime Minister Dmitry Medvedev for "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 later face-off between police and protesters last Wednesday, it has broadened into an outpouring of anger against perceived sleaze and corruption in the country Yanukovich has led for four years.
BATTLE FOR SOUL
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'.
McCain, who also met opposition leaders - the former boxing champion Vitaly Klitchko, former economy minister Arseny Yatsenyuk and far-right nationalist Oleh Tyahnybok - said: "We ... want to make it clear to Russia and Vladimir Putin that interference in the affairs of Ukraine is not acceptable to the United States."
Speaking to journalists after addressing crowds, he said it was disturbing to hear that the EU may be suspending talks with Ukraine on the trade and political agreement.
Yanukovich seems likely to be able to hang on to power despite the strength of the crowds at weekend rallies. But much may depend on what sort of deal he can cut with Putin on Tuesday and how quickly it will help the Ukrainian economy.
Whatever the outcome, his popularity has suffered hugely from the crisis, the opposition has been re-energised, the faith of key stakeholders such as the oligarchs has been shaken and he can no longer assume re-election in 2015.
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 at the Kremlin talks on Dec. 17 should 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.
On Sunday, the crowds gathered on Independence Square were smaller than a week before but no less determined.
"I am here against the criminal authorities, joining Europe is a secondary goal," said Oleksander Vdovin, 25, an engineer in Kiev wrapped in a Ukrainian flag.
Yanukovich's supporters have also staged rival rallies nearby on Saturday and Sunday.
"We are here because an effort to destabilise the country has begun. I voted for the president, I'm here to back him," said Nikolai, 61, who works in the southern Ukrainian port of Kherson.