BRUSSELS (Reuters) - The European Union's top court on Wednesday dismissed a Polish and Hungarian challenge to a new sanction that would cut funding to member countries which violate democratic rights and freedoms.

       The final ruling by the Luxembourg-based European Court of Justice marks a milestone in the EU's feuds with populist rulers in Poland and Hungary, who stand accused of undercutting democratic rights and values.

       At stake are hundreds of billions of euros of funds, the EU's internal cohesion, and international standing.

       Warsaw and Budapest - where Prime Minister Viktor Orban faces a tightly contested April 3 election - deny wrongdoing and accuse the EU of imposing liberal values alien to what they say are their traditional, conservative and Catholic societies.

       Thirty-six billion euros ($41 billion) in pandemic recovery funds earmarked for Poland, and 7 billion euros for Hungary, are already frozen over their track record on democratic rights and values.

       It will now take weeks for the EU to formally start the process of cutting handouts and several months of political horsetrading are expected.

       "It is highly likely that the mechanism will be triggered against Hungary, probably in March, but not yet against Poland," said Mujtaba Rahman of the Eurasia Group consultancy.

       "It will take several months for the process and politics to play out, meaning any suspension of EU budget funds is not likely until the third or fourth quarter of this year - if at all."

       ($1 = 0.8786 euros)

       (Additional reporting by Jan Strupczewski; Editing by David Holmes)