* Tens of thousands gather for weekly rally
* Turnout down on previous weeks
* Opposition leaders turn focus to next election
By Olzhas Auyezov
KIEV, Dec 29 (Reuters) - Tacitly acknowledging that street protests would not topple Ukrainian President Viktor Yanukovich, one of his leading rivals told demonstrators on Sunday that the opposition would steer the country back towards Europe after winning the next election in 2015.
Tens of thousands of people gathered on Kiev's Independence Square for what has become a weekly event since late November, when Yanukovich's government refused to sign an association agreement with the European Union and turned instead to Russia for an economic rescue package.
The turnout was visibly lower than last week, when it was estimated at about 100,000, as many Ukrainians were busy preparing for the New Year holidays and the Ukrainian Orthdox Christmas, which is celebrated on Jan. 7.
The falling numbers have eased the pressure on the government, which is pressing ahead with forging closer ties with Russia, having secured a $15 billion bailout package from Moscow and a discount on vital Russian gas supplies.
The opposition wants the country of 46 million people to move closer to Europe and escape the grip of Russia, its former imperial master.
"We are preparing to win the presidential elections," said Arseny Yatsenyuk, the leader of the opposition Batkivshchyna (Fatherland) party. "We are building a team... that will be able to turn Ukraine into a European country."
An opinion poll published this week by the local Democratic Initiative foundation showed that, if a presidential election was held now, Yanukovich would lose in a second round run-off to heavyweight boxing champion Vitaly Klitschko, or indeed to any of several other opposition leaders including Yatsenyuk.
On Sunday, opposition supporters in hundreds of cars headed for Yanukovich's residence just outside Kiev but were met by police on the road.
Klitschko and other opposition leaders appear unwilling to end the street protests, even as they lose steam.
Klitschko called for a general strike after the holidays and, together with other opposition leaders, urged supporters to gather at the square again on New Year's eve.
"We will fight to the end, we will not leave," he said. (Additional reporting by Pavel Polityuk; Editing by Mark Trevelyan)