* Gazprom says final offshore investment decision approved
* Junior partners can leave if conditions not fulfilled
* Engineering, environment, regulatory work still to be done
* Total investments seen at 16 billion euros (Adds consortium statement saying FID leaves partners right to opt out)
By Vladimir Soldatkin and Tsvetelia Tsolova
MOSCOW/SOFIA, Nov 15 (Reuters) - A Gazprom-led consortium made a final investment decision to build the 16 billion euro ($20.47 billion) South Stream undersea gas pipeline to Europe, but left its junior partners the right to exit if key practical steps were not made.
The decision late on Wednesday aims to preserve Russia's dominance of the European market.
Gazprom separately signed a final investment decision with Bulgaria for a stretch of the pipeline, bowing to a demand for gas price cuts to the Balkan country in return for the deal.
Gazprom's insistence on pressing ahead with the pipeline shows its determination to hang onto its core European market and to get a jump on rival pipeline projects to carry gas to southern Europe from central Asian producers.
But the project is faced with falling demand and pressure from the European Union, which is conducting an antitrust investigation of Gazprom.
Furthermore, the estimated 16 billion euro cost for South Stream is seen as high, and its status is unclear under the European Union's Third Energy Package, which bars suppliers from owning transportation capacity.
Gazprom, which is expected to fund half of the total capital expenditures according to its share in the project, did not disclose the financial outlays, which according to some analysts may exceed 25 billion euros once the onshore sections are built.
The South Stream Transport consortium said in a statement the decision had been made subject to approval by its board of directors and board approval and the partners would aim to transport the first gas on schedule in 2015.
"The minority shareholders maintain the right to leave the project in case certain conditions will not be satisfied in the future," the statement said.
In addition to broader questions of demand and EU regulations, the consortium has yet to complete engineering and environmental impact studies and to sign a commercial agreement among the partners, as well as clear other regulatory hurdles.
The pipeline was designed to reduce the risks of shipping gas across Belarus and Ukraine, which have had a number of price disputes with Russia, some of which have led to cuts in supplies to Europe through existing pipelines.
"South Stream's contribution into providing Europe with energy security is very significant. It allows us to create alternative and secure natural gas supply routes to our consumers," Gazprom Chief Executive Officer Alexei Miller said in a separate statement which did not mention the right to exit.
The construction of the project, whose offshore section will stretch 900 kilometres across the Black Sea, will begin on Dec. 7.
Gazprom and its partners including France's EDF, Germany's Wintershall and Italy's Eni ruled in the final investment decision that the pipeline would terminate in Italy at Tarvisio, the entry point to its pipeline network.
The map on the project website, showing Tarvisio, is based on the final investment decision, a Gazprom spokesman said.
That decision may have encouraged Eni, Gazprom's largest partner in the group, to press ahead with the project. The other option under consideration was Austria, whose OMV is a member of the rival EU-backed Nabucco consortium.
To get to the decision, Gazprom has already had to overcome scepticism and opposition by some countries whose territory will be crossed by the pipeline.
In Sofia, Bulgarian President Boiko Borisov, who came to power promising to get a better energy deal from Russia, said at a press conference with Miller to announce the decision that Bulgaria would have a 20 percent discount on Russian gas from January 1. ($1 = 0.7817 euros) (Editing by Melissa Akin and James Jukwey)