* Gazprom says 12.5 bln euros needed for domestic upgrade
* Earlier said 16 bln for sections under sea, land in Europe
* New gas spat between Russia and Ukraine flares up
MOSCOW, Jan 29 (Reuters) - Russia's Gazprom said it must invest around 12.5 billion euros ($16.8 billion) to make its domestic gas pipeline system compatible with the planned South Stream undersea link to Europe, increasing the project's already heavy cost.
The additional expense pushes the overall cost to 29 billion euros for the South Stream project under the Black Sea, which is designed to bypass countries such as Ukraine and Belarus. The bulk of Russia's gas exports to Europe currently must pass through them.
Many analysts say Gazprom is saddled with inefficiency, high costs and an inflated investment programme. Russia's gas export monopoly had earlier estimated costs for South Stream at 16 billion euros, including 10 billion for its subsea section.
Gazprom has additionally earmarked 509.586 billion roubles ($16.9 billion) of its long-term investment programme for an upgrade of its domestic pipeline system as part of the project, the company said on its website late on Monday.
Disputes over gas prices between Russia and Gazprom in the height of the winters of 2006 and 2009 led to cut-offs in gas exports to Europe, which gets over a third of its gas from Russia.
Their dispute flared up again over the weekend when Ukraine said that Gazprom had hit it with a $7 billion bill for alleged arrears under a long-term contract.
Construction of South Stream, with an offshore section that which will stretch 900 kilometres under the Black Sea, began on Dec. 7. The official launch of gas flows is scheduled for late 2015 at an annual pace of 15.75 billion cubic metres, with full capacity of 63 bcm to be reached in 2018.
Gazprom said the bulk of its investment in the domestic pipeline, 232.1 billion roubles, will be spent to increase the capacity of a trunk line from Ukhta in the north of Russia to Torzhok, some 230 kilometres (144 miles) north of Moscow.
Gazprom's partners in the South Stream project - France's EDF, Germany's Wintershall and Italy's Eni - will help cover half of its initial 16 billion euro cost but not the costs of its domestic upgrade.
($1 = 30.1805 Russian roubles)
$1 = 0.7429 euros Reporting by Vladimir Soldatkin; Editing by Maria Kiselyova and Jane Baird