Local media claimed the eight-team competition, which includes Spain and Italy as well as the hosts, could be stopped after an estimated one million people protested in cities across Brazil on Thursday.
However, a FIFA spokesman told Press Association Sport: "To date, neither FIFA nor the LOC (local organising committee) have ever discussed any such possibility."
The Confederations Cup is a test event for next year's World Cup in Brazil but has become the focus for nationwide protests against rising costs, including bus fares, government corruption and spending on the 2014 tournament.
Police on Thursday fired tear gas and rubber bullets at crowds that had broken through barriers in Fortaleza and Salvador, in north-east Brazil. Brazilian broadcaster O Globo said stones were thrown at FIFA's hotel in Salvador and two windows were broken, and two buses serving the world governing body damaged.
There was also violence in Rio de Janeiro, where protesters stormed the stage of a concert aimed at showcasing the Confederations Cup.
Local media also reported that one of the eight teams was putting pressure on its leaders to pull out of the tournament due to fears for the safety of players' relatives, but a FIFA spokesman said it was not aware of any such situation.
FIFA later issued a statement which read: "We support and acknowledge the right of free speech and to demonstrate peacefully and condemn any form of violence. We are in constant contact with the local authorities and have full trust in the security arrangements in place.
"We will continue to monitor the situation. At no stage have either FIFA, the Local Organising Committee (LOC) or the Federal Government discussed or considered cancelling the FIFA Confederations Cup.
"We are in constant contact with all stakeholders, including the teams, and keep them updated on all arrangements made. We have not received any requests to leave Brazil from any team."