Aldo Rebelo said work at all but one of Brazil's 12 venues was now on schedule and promised that other infrastructure, including airports, could handle the expected number of visitors.
He also defended cut-price tickets for low income families and Brazil's native Indians, an issue which has divided the Brazilian government and football's governing body FIFA.
"People might think that I'm exaggerating, but my impression is that if Brazil had to organise the World Cup in two months' time, we would be ready," Rebelo told the programme "Good morning, Minister" on the government-run NBR channel.
"We can do everything which is planned for the World Cup," added Rebelo, appointed in October to replace Orlando Silva who quit over corruption allegations.
Rebelo said the only stadium which had fallen behind schedule was the Beira-Rio in Porto Alegre, where work has been paralysed for nearly six months.
This has followed a disagreement between Internacional, the club which own the stadium, and construction companies due to carry out the refurbishment work.
INDIGENOUS POPULATION
Rebelo played down media reports of disagreements between FIFA, which wants full control over ticket prices, and Brazil's Congress, which wants price reductions for certain sections of the population.
FIFA has told Brazil to pass a law implementing its conditions, drawing opposition from Congress where some politicians have seen the demand as an affront to the country's sovereignty.
"We are all making a common effort but it's natural to have differences in any given activity," said Rebelo.
"As well as tickets for senior citizens and students, I have asked for a portion of tickets to be set aside for low incomes families and the indigenous population.
"Half price would not resolve the matter because that is still too high for their income.
"It would not make sense to hold the World Cup in Manaus and not allow the indigenous population to see the games," he added, referring to the city situated in the heart of the Amazon rain forest.
He added that Brazil was used to staging big events and that airports could cope, even if they were handling more than their planned capacity.
"The carnival in Rio de Janeiro mobilises more people in a week than we will have at the World Cup," he said.
"Salvador and Recife also have a much bigger presence for their carnivals."
Rebelo's interview came one day after former Brazil striker Ronaldo joined the Local Organising Committee in an attempt to boost its public image.
