Anti-government protests hit a fever pitch last June during the Confederations Cup, with around a million people pouring into the streets on a single night demanding better schools, hospitals and an end to corruption, along with bitter complaints about the billions of dollars being spent to host the World Cup.
In recent months, the demonstrations have shrunk in size but remain violent, with anarchist adherents to the "Black Bloc" protest tactic repeatedly clashing with police and carrying out vandalism during protests in Rio de Janeiro and Sao Paulo. A TV cameraman was recently killed while covering a protest in Rio after being hit in the head with a flare allegedly fired by a protester.
Despite the continuing incidents, Valcke said he's not worried that football's premier event will hit any stumbles, telling a media conference that "we are expecting a quiet World Cup and we are expecting that whoever wants to be at the World Cup will have the right to do so."
No matches were delayed during last year's Confederations Cup, although protests raged near the stadiums on several occasions. Police maintained a security ring around the stadiums that mostly kept protesters at bay, although on a few occasions groups did break through. Officers used tear gas and rubber bullets on protesters outside Rio's famed Maracana stadium even as Brazil downed Spain 3-0 during the championship match last year.
More demonstrations are certain during this year's World Cup, yet Valcke insists that the tournament's importance will outshine protests.
"We are sure that the World Cup is too big an event for any country around the world not to support its organization," Valcke said. "I'm not saying to support FIFA, that's not the point, (but) to support the organization of these games in a country in 12 host cities."
Recent protests have turned violent mostly because of the anarchist movement called Black Bloc, which has already scheduled street demonstrations during the World Cup.
"You can have pacific demonstrations, it's a right in any democracy around the world," Valcke said. "But in non-pacific demonstrations, when people are just trying to create problems, just trying to fight the authorities, there is only way to bring it down. The police need to make sure that these people will be under control."
Brasilia was one of the host cities which endured violent protests during the Confederations Cup.
Valcke visited the capital's stadium as part of his latest inspection tour. Later on Monday he went to the southern city of Porto Alegre, where the president of the Brazilian club in charge of the Beira-Rio stadium said there was a risk the venue would be unavailable for the World Cup because of a dispute over who will pay for the temporary facilities required by FIFA outside the venues.
Valcke met with local officials and said they made a commitment to find a solution by Thursday.
"FIFA and the LOC (local organizing committee) would like to reiterate that this is not a question of Porto Alegre being, or not being part of the 2014 FIFA World Cup," FIFA said in a statement. "The stadium is ready to host normal football matches. The challenge is the transformation of the arena to be able to host FIFA World Cup matches. All parties are committed and working hard to find a solution for the issue of the complementary structures."
On Tuesday, FIFA will announce whether Curitiba in southern Brazil will remain a tournament host venue. FIFA gave an ultimatum to local officials, and they have one day left to show its delayed stadium will be ready in time.
In addition to Curitiba and Porto Alegre, three other host cities have stadiums under construction even though Brazil promised to have all 12 venues ready by the end of last year.
AP Sports Writer Tales Azzoni in Sao Paulo contributed.