The decision must next be confirmed by a court in Hungary.
Emfesz will appeal the decision in Sweden and in Hungary, Emfesz CEO Istvan Goczi told the paper.
The court in Stockholm ruled Emfesz must pay USD 269.5 million for gas delivered in 2008 and USD 106.2 million for gas delivered in January-April 2009, plus interest. It must also pay USD 151.2 million on invoices from 2005-2007.
RosUkrEnergo is a joint venture established earlier by Russia's Gazprom and Ukrainian businessman Dmitry Firtash to sell Russian gas in Europe. The company was cut out of the picture in 2009, after Kiev and Moscow reached an agreement that removed the middleman from sales of Russian gas delivered through Ukraine.
The deal left Emfesz without its supplier, but the company still managed to take delivery of 350 million cubic metres of gas between January and April of 2009.
Mr Goczi, availing of an earlier authorisation, later sold Emfesz to Rosgaz, a Russian-owned company registered in Switzerland, for a token price of USD 1.