"The parties discussed possible construction of a gas lateral from South Stream to the Republika Srpska," the Russian company said in a statement.
Miller later signed a memorandum of understanding with Serbian President Boris Tadic for the eventual long-term purchase and sale agreement for 70 billion cubic feet of natural gas.
Gazprom said constructing the Serbian section of South Stream would create 2,200 jobs and result in about $2 billion in direct investments to the country.
South Stream would split with arteries headed to Greece and the Balkans after passing through the Turkish waters of the Black Sea. It would carry roughly 2.2 trillion cubic feet of gas per year when it goes into service by 2015.
Moscow aims to find new ways to get natural gas to European consumers. Disputes with Ukraine, which hosts the bulk of Russia's gas bound for Europe, makes traditional routes risky.
Notable deaths of 2014 [PHOTOS]
EIA: Russia diversifying energy production