* Naftogaz debt relates to 2009 gas deal
* IMF chief says Russia could stop strain on Ukraine budget
* Ukraine is appealing Swedish court ruling
YALTA, Ukraine, Oct 2 (Reuters) - International Monetary Fund chief Dominique Strauss-Kahn proposed on Saturday that Russia help Ukraine repay a nearly $3 billion debt to former gas trade intermediary RosUkrEnergo.
A Swedish arbitration court ruled in June that Ukrainian state energy firm Naftogaz must give back to RosUkrEnergo, a firm owned by Ukrainian tycoon Dmytro Firtash and Russian gas giant Gazprom, 12.1 billion cubic metres of gas that it said were "expropriated" in 2009.
Ukraine's government said last year it had bought the gas in question from Gazprom for $1.7 billion. Under its current deal with Russia, the gas would be worth about $2.8 billion.
The claims from RosUkrEnergo followed a decision by Ukraine and Russia to scrap the firm as an intermediary between Gazprom and Naftogaz after a series of rows that briefly halted transit of Russian gas to Europe.
Ukraine's government has lost a first appeal against the Swedish court ruling, filed in a local court.
Strauss-Kahn, speaking at a conference in the Ukrainian Black Sea town of Yalta, said the government needed to find a solution that would not put the budget under pressure by a straightforward cash payment.
"If this is confirmed by a local court ... it is a stress to the fiscal balance," he said.
Strauss-Kahn said Russia could also contribute to a solution. "Maybe it would be fair if both sides took part," Strauss-Kahn said, though he added that Russian Finance Minister Alexei Kudrin has in the past refused to consider this option.
Under a $15 billion deal with the IMF agreed in July, Ukraine needs to stick to strict budget deficit targets, a requirement that has already forced the government to take unpopular measures such as raising domestic gas prices.
(Reporting by Olzhas Auyezov; Editing by Richard Balmforth and Jane Baird)