Organisers of a Day of the Dead party in Moscow's Red Square say a decision to cancel the parade was taken after Russian authorities intervened.
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Mexican football fans - whose team is one of the 16 to make it through to the World Cup knock-out stages - had planned a party in the zone set aside for them in the city, followed by a street parade to Red Square several hundred metres away.
But one of the organisers said they were told by authorities after midday on Friday to hold the parade and event indoors, declining to explain why.
Sergei Malinkovich, deputy head of the Communists of Russia party, said people dressed as skeletons - one of the traditional symbols of the Mexican annual holiday at which families honour their dead loved ones - should not be allowed to march on what his party has called "hallowed" ground.
"Why should we have some kind of skulls there?" Malinkovich said.
The body of Soviet founder Vladimir Lenin lies embalmed in a marble tomb on the square and Soviet leaders and dignitaries are buried in the Kremlin walls.
Malinkovich's party had appealed to the Interior Ministry to stop fans holding the parade, he said, arguing it could provoke violent clashes with Russian patriots.
"Russian people on the square would almost certainly have tried to stop them. There would have been conflicts to say the least, and perhaps clashes," he said.
The event - held four months before the actual celebrations in Mexico - was held in the fan area and was attended by several hundred revellers.
