* 50,000 demonstrate in Varna
* Protesters fail to unite behind single leader
* Elections due on May 12
SOFIA, March 3 (Reuters) - Tens of thousands of Bulgarians furious over poverty and corruption protested in more than a dozen cities on Sunday, as a lack of clear support for any political party mired the country in limbo days after the government was toppled.
Prime Minister Boiko Borisov quit along with his centre-right government on Wednesday after two weeks of sometimes violent protests. He remains in office until an interim government is appointed, most likely next week, which will take Bulgaria to elections due on May 12.
However Bulgarians are still struggling to unite behind a single political leader or give voice to a clear set of demands.
Polls suggest neither Borisov's rightist GERB party nor the opposition Socialist Party has enough support for an overall majority, and whichever wins the election will have to try to assemble a coalition to form a working government.
Thousands of people took to the streets of cities including the capital Sofia, Plovdiv, Burgas, Blagoevgrad, Ruse and Sliven on Sunday - a national holiday. In the biggest rally, about 50,000 protested in the Black Sea city of Varna, local media reported.
"It is obvious that the protesters are not united and this could very quickly destroy the enthusiasm of the people," said Georgi Trendafilov, a demonstrator in Sofia downtown.
Six years after joining the European Union, Bulgaria trails far behind other members. Its justice system is subject to special monitoring and it is excluded from the passport-free Schengen zone because of other members' concerns about graft.
The country's public debt is one of the lowest in the bloc but business cartels, corruption and wages that are less than half the EU average, have kept many from feeling the benefit.
It also has the cheapest electricity costs in the EU but an increase in prices since last July under an energy market liberalisation has made it harder for Bulgarians to heat their homes through a cold winter.
The demonstrations began with a handful of youngsters protesting against high electricity bills. Eventually, hundreds of thousands of Bulgarians took to the streets, angered by their low living standards.
President Rosen Plevneliev said an interim government would aim for stability by sticking to the 2013 budget, which foresees a deficit of 1.3 percent of GDP, and implementing previous commitments such as a 9 percent increase in pensions from April.
He also said he would set up a 35-member public council to advise the interim government and re-present the people's interests. But consultations for the establishment of the council at the presidency collapsed on Saturday.
Representatives of protesters, objecting to the inclusion of some wealthy businessmen, walked out of the talks. They said they could not "sit at the same table with those they were fighting".
"We are going out to fight until the end, we will not negotiate with oligarchs," said Angel Slavchev, one of the leaders of the demonstrations. A trade union leader also quit, objecting to the composition of the council.
Earlier this week, Borisov, described as "a lone player" by analysts, dismissed the idea of a governing national unity coalition and said such a move could benefit nationalist parties such as far-right Attack.
Support for Borisov's rightist GERB party has fallen over the last year, and it is now neck-and-neck with the opposition Socialist Party.
Just before resigning, Borisov had proposed to cut electricity prices by 8 percent and alarmed investors by saying the government would revoke the distribution licence of the Czech utility CEZ, risking a diplomatic row with the Czech Republic and EU.
The energy regulator proposed a smaller, 6.4 percent cut on Friday, a few days after CEZ and the other two distributors, Austria's EVN and the Czech firm Energo-Pro, said they had done nothing wrong.