"The stadium is 97 percent ready," said Andres Sanchez, the former Corinthians president who is overseeing construction of the Arena Corinthians.
"We have some things pending because of the accident but we've got the all-clear and by the end of the month they will remove the damaged piece. We will hand the stadium over by April 15."
FIFA said on Monday it was delighted with the progress made although secretary general Jerome Valcke pointed out the stadium was supposed to be ready last month.
"We are very happy with what we've seen today," added Valcke. "A lot of work has been done, a lot of work has still to be done where the accident took place, but we are very confident that all is on track."
The stadium on the outskirts of Sao Paulo is one of the most expensive of the 12 World Cup venues and was one of the last to get started.
Two workers died in November when a crane moving parts of the roof into place toppled over and the delivery date was subsequently put back four months.
The fallen structure, a massive 420-ton piece of metal tubing, is still where it fell, leaning against one side of a stand.
When asked how the venue could be deemed 97 percent ready when a large part of the roof was still clearly damaged, the stadium's chief engineer told Reuters the affected area was relatively minor.
"It's a very small part," said Federico Barbosa. "Everything else is done or almost done."
The delays at the venue that will stage the opening match between Brazil and Croatia on June 12 is one of the issues affecting the country's preparations to host the first World Cup in South America since 1978.
None of the six stadiums that were due to be finished in December were ready on time. Six were completed last year and used in the Confederations Cup test event.
Public transport projects in several cities have also been abandoned or scaled back and there is concern new terminals at some airports will not be ready.
Valcke said he would only talk about other venues after visiting them on this his first visit to Brazil in 2014.
He travels to Cuiaba later on Monday and then to Curitiba on Tuesday.
Valcke flies to Natal on Wednesday when he will attend the opening ceremony of the Arena das Dunas.
He said he would spend a week each month in Brazil until the competition begins.
- Sports & Recreation
- Jerome Valcke