The game was due to be played in Madrid's Bernebau stadium on December 9, but the club have released a statement saying it will leave ticket holders from the original match out of pocket.
"The club maintains that the change of venue and decision distorts the competition, harms those who acquired a ticket and affects the equality of conditions," said River Plate in a statement.
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As a result, River are refusing to take part in the second leg of the final having drawn 2-2 against their Buenos Aires rivals in the first leg.
The decision to move the game out of Argentina was taken after River fans threw missiles at Boca Junior's team bus, causing injuries to several players.
The game was initially rescheduled for the following day before CONMEBOL also postponed that game.
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