Only six of the 12 stadiums hosting the tournament have been completed, while infrastructure, cost and safety remain ongoing concerns with less than eight months remaining.
The latest setback came on Saturday, when four fans were shot just outside the host city of Natal before a second division match between America and Ceara.
Valcke, though, has downplayed concerns over the tournament and remains confident it will be a success.
"We are working hard and we are working with what we have now in Brazil to make sure that the World Cup will be a great tournament and it will be a great tournament," he said in central London on Sunday.
"We are focusing on the final draw and we are sure that the 12 stadiums will be ready. We are working on the quality of the pitches.
"It will work. You have seen we have some issues regarding the price of air fares and prices of accommodation, so there are quite normal discussions we must have before the tournament.
"I will not talk about the legal side of some issues we are facing in Brazil because they are ongoing cases, so there is no way I could comment."
Asked about the fan violence outside Natal, Valcke added: "It is not the first time there is violence around the stadium.
"Once it was even worse between a referee and a player. It is a fact and it is happening in Brazil - a huge country, where football is a passion.
"You cannot control everything but what I can say is when it is a World Cup I know these kind of things would not happen because we have the highest level of security you can imagine around the organisation of this tournament."