"To date, neither FIFA nor the local organising committee have ever discussed any such possibility of cancelling the FIFA Confederations Cup," FIFA said in a statement sent to Reuters.
In a later statement it added: "FIFA in constant contact with all stakeholders, including teams. FIFA has not received any requests to leave Brazil, from any team.
"FIFA is in constant contact with local authorities. Have full trust in security arrangements and we'll continue to monitor situation.
"FIFA supports and acknowledges the right of free speech and to demonstrate peacefully and condemns any form of violence."
CBN radio and the website of the Estado de Sao Paulo newspaper, both respected, mainstream Brazilian media, carried reports earlier on Friday speculating that the eight-team tournament, considered a dry run for next year's World Cup, was in danger.
"FIFA will claim compensation from Brazil if the Confederations Cup has to be suspended," said a headline on CBN's website.
An estimated one million people took to the streets in cities across Brazil on Thursday as the country's biggest protests in two decades intensified despite government concessions meant to quell them.
The protests, now in their second week, have been about high taxes, inflation, corruption and poor public services and have also targeted the $26 billion of public money being spent on the World Cup and the 2016 Olympics.
A CBN report said one of the eight teams were pressuring their leaders to leave the Confederations Cup because they were worried about relatives who were in Brazil to watch the matches.
"On the legal side, there's a certain degree of confidence on FIFA's part that if the tournament is cancelled, it can launch a claim from the Brazilian government, if there are no safety guarantees for the competition or the World Cup," said the report by Juck Kfouri, a veteran Brazilian sports journalist.
"There is strong speculation, which won't go away," he added, referring to rumours that the competition was in danger.
The Estado said that FIFA was negotiating with the teams to try to persuade them to stay.
"The protests in the streets of Brazilian cities have forced FIFA to negotiate with the teams to keep them in the Confederations Cup," it said.
"By law, if there is no guarantee of safety, it could force the tournament to be cancelled."
The Estado said that two FIFA vehicles were attacked in Salvador, where Uruguay played Nigeria on Wednesday, and its employees had been instructed not to wear uniforms outside their hotel.
FIFA confirmed the incident but said the vehicles were empty and parked in the street when the windows were smashed.
The Folha de Sao Paulo said that FIFA and the participating teams were "terrified" by the situation.
"The competition has become a nightmare for the organisation," it said. "FIFA didn't imagine that the event would be perfect but the size of the problems is worse than the worst-case scenario."
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