* Senator John McCain backs anti-government protesters
* President Yanukovich supporters see him as guarantor of stability
* Mass protests against Yanukovich in their fourth week
* Fear of violence as rival rallies in close proximity (Recasts with McCain)
U.S. Senator John McCain met Ukrainian opposition leaders in Kiev on Saturday and voiced support for protesters camped out for weeks in the capital, a move sure to anger Moscow for what it sees as Western meddling in its backyard.
The street protests started after the Nov. 21 decision by President Viktor Yanukovich - seeking the best possible deal for Ukraine to stave off bankruptcy - to walk away from a trade pact with Europe at the last minute and seek closer ties with its old Soviet master.
The movement has since grown in size and vehemence, bringing tens of thousands onto the streets in a series of rallies, becoming an all-out protest against the president and his cabinet.
McCain is the latest of a string of European and American dignitaries to tour the sprawling protest camp set up behind tall barricades - prompting Russia to accuse the West of excessive involvement.
McCain was due to be joined by the chairman of the Senate's Europe subcommittee, Chris Murphy, on Sunday.
"I am proud of the people of Ukraine and their steadfast efforts for democracy," McCain told reporters after meeting the country's Foreign Minister Leonid Kozhara.
McCain then met opposition leaders - the ex-boxing champion Vitaly Klitchko, former economy minister Arseny Yatsenyuk and far right nationalist Oleh Tyahnybog - who are calling for Yanukovich's government to resign and for early elections.
Police violence on Nov. 30 against what was initially a pro-Europe demonstration shocked Ukrainians, setting a match to deep-seated anger over corruption and sleaze.
U.S. Democrats and Republicans have condemned the harsh measures and on Friday senators issued a resolution calling for the United States to consider sanctions in case there is further violence against peaceful demonstrators.
"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.
Thousands of Yanukovich supporters staged a rival rally in Kiev on Saturday, many bused in from Donetsk and other cities in eastern Ukraine - the traditional stronghold of the president's Party of Regions.
"We are here to support the president and stability," 18-year-old Maria Nikolayeva said, holding the Party of Regions blue flag. "Yanukovich is our best prospect at the moment ... I don't see any alternative."
In an attempt to defuse weeks of unrest, Yanukovich on Saturday dismissed the head of Kiev's state administration and a national security aide over the violence on Nov. 30. Prosecutor General Viktor Pshonka said two more police officials involved that night were under investigation.
But protesters continued to stream into the capital for the weekend protest. Talks between the government and the opposition on Friday appeared to go nowhere.
Sweden's foreign minister said Russia should not feel threatened if Ukraine moved closer to the European Union.
"Ukraine has a free trade agreement (FTA) with Russia and we have nothing against that," Carl Bildt told Reuters on the sidelines of a conference in Monaco.
"Why should they object that the Ukraine has an FTA with the EU? It is a win-win for Ukraine and Russia. Why they should see everything as a zero sum game? It's not," said Bildt, who was closely involved in EU talks with the Ukraine.
TENSIONS IN THE CAPITAL
The proximity of rival demonstrations in Kiev - separated only by a line of riot police - raised fears of fresh violence.
"The most difficult matters should and can only be solved at the negotiating table. People should not be driven away from their work, from their families," Prime Minister Mykola Azarov told supporters. "Let's tell the people to go back home to their families and their business."
Sergei Bychok, a 43-year-old electrician, said he came to the pro-government rally because he wanted stability.
"I got my salary but a lot of people are here because they are afraid they won't," he said in a whisper, referring to widespread accusations among Yanukovich opponents that the authorities paid or pressured people to attend their rally.
In the square held by the anti-government protesters - now known as the "Maidan", meaning "Square", or the "Euro-maidan" - the atmosphere was peaceful.
For those who stayed overnight, the day began with early morning prayers followed by an aerobics session led from the stage. The crowds grew denser towards the evening with people holding up placards picturing Yanukovich and Azarov behind bars and sporting stickers reading "Raise Ukraine!".
"I'm here for Europe and against Yanukovich. For me it's almost the same because it's the European Union association that is our chance to rid Ukraine of corruption," said Oleh, a 22-year-old engineering student. "We will be here a month or as long as it takes."