* Bulgaria to push for entry to EU banking union -president
* New PM Bliznashki pledges transparent government
* Construction on South Stream frozen for now -president
* No solution in sight to banking crisis (Adds quotes, details, background)
SOFIA, Aug 5 (Reuters) - A Bulgarian law professor and former Socialist lawmaker was named caretaker prime minister on Tuesday until the next election, as the Balkan state grapples with the fallout of its worst banking crisis since the 1990s.
Georgi Bliznashki, 57, took over as premier while Rumen Porozhanov, a 49-year-old former senior civil servant, will be finance minister, President Rosen Plevneliev said in a televised statement to the nation.
The interim government follows the resignation of the Socialist-led coalition at the end of July, paving the way for a snap election on Oct. 5, the second in less than two years.
Bliznashki inherits a raft of problems to sort out. In the past year, Bulgaria has struggled with sluggish economic growth, months of street protests against corruption, a diplomatic dispute over the Russian-led South Stream pipeline, deadly floods and a sovereign credit rating downgrade in June.
Most pressing is the fate of Corporate Commercial Bank (Corpbank), Bulgaria's fourth largest lender, which was hit by a run on deposits in June. It remains shut pending a full audit into its books ordered by the central bank.
Efforts by the outgoing government to rescue the lender were scuttled by parliament last month, and there is no agreement yet on to what extent the bank's depositors and bondholders will be protected in a possible state rescue.
Making matter worse, lawmakers on Monday blocked a proposal for the interim government to raise new debt that could have been used to rescue Corpbank, limiting Bliznashki's options to solve the crisis.
"In conditions of political crisis, we will work for more stability, dialogue and transparency in governance," Bliznashki told reporters.
Corpbank's problems have put renewed scrutiny on the investment climate in Bulgaria, the European Union's poorest member state and one of its most corrupt. Holders of dollar denominated bonds, which mature on Friday, may sue the government if they don't get their money back.
The interim government will get the ball rolling for Bulgaria to join the EU's banking union, work to unfreeze blocked EU aid, and prepare a revision plan for the budget, Plevneliev said.
The president had appealed to parliament to allow his government to raise new debt and make changes to the budget, warning that a failure to do so would hamper his administration and risked hurting the economy.
The debt could also have been used to pay workers at state-run construction projects and pay fines to Brussels in order to unfreeze EU aid programmes.
"Unfortunately the parliament in its last days remained deaf to the necessary revision of the budget ..." Plevneliev said.
"The responsibility will lie not with the interim government but with those who, led by their tactical considerations and party propaganda, missed the interest of the Bulgarian people."
Bliznashki was formerly a senior member of the Socialist party but was kicked out earlier this year, after he openly endorsed an anti-government, anti-corruption student occupation of Sofia University.
An outspoken critic of the outgoing coalition, Bliznashki also drew fire from his party by becoming the head of a committee that collected over 560,000 signatures to support an initiative by the president for voting reform.
Porozhanov has held various positions at the finance ministry and was also on the supervisory board of the state-controlled Bulgarian Development Bank until last month - one of two institutions invited to help rescue Corpbank.
Bliznashki will also have to decide whether to approve an agreement with Westinghouse Electric Company - signed by the outgoing government - that enables the construction of a new nuclear reactor estimated to cost $5 billion.
The agreement would help Bulgaria reduce its energy dependence on Russia at a time of increased tensions between Moscow and Brussels over Ukraine. Bulgaria at present is one of five EU states totally dependent on Russia for nuclear fuel.
Plevneliev further said that construction work on South Stream, a pipeline that would pump 63 billion cubic metres of gas per year to Europe via the Black Sea, bypassing Ukraine, would remain frozen until Brussels green-lights the project.
The main opposition GERB party, which had ruled the formerly communist country until it was brought down by street protests in February 2013, is tipped to win the October election.
Bulgaria has been dogged by two years of political instability, which prompted Standard & Poor's to downgrade its sovereign credit rating to one notch above junk in June.
Plevneliev also said his government would nominate Kristalina Georgieva as Bulgaria's candidate for the next EU Commission, without specifying for which post. Georgieva is seen as a possible contender for the EU's foreign policy chief. (Additional reporting by Angel Krasimirov; Editing by Mark Heinrich)