Speed said the ICC was happy with what the world governing body had seen in the run-up to the March-April tournament, the first time the World Cup is to be held in the Caribbean.
"There is still much to be done. The message we bring is that we are very happy with progress but we cant relax," said Speed.
"There must be great attention to detail as the venues come out the ground."
The build-up to the event has been dogged by worries over construction delays as well as the price-hikes introduced by hotels aiming to cash in on the marathon event which will draw thousands of extra tourists to the area.
New ICC President, Percy Sonn, claimed that the West Indies is further ahead than South Africa was in 2003, the venue for the last tournament.
"I think the West Indies is, relatively speaking, ahead of where South Africa was, vis-a-vis the final stages of this phase, given that they (the West Indies) are building new stadiums," said the South African-born Sonn.
"South Africa didn't build any new stadiums - they just improved on the old stadiums. I think the West Indies are fine and further than where South Africa was."
Organising committee chief executive Chris Dehring described the region as the "spiritual embryo of one-day cricket," and highlighted the overwhelming worldwide interest in the tournament as the main reason for the accommodation demand being so strong.
However, he said he is confident there will be enough of a variety of accommodation ranging from bed and breakfast programs, cruise ships and hotels for fans to choose from.
"I think this will be the most cosmopolitan Cricket World Cup. We will see people from more countries attending this World Cup than any others before," he declared, alluding to the fact that people from 124 countries have applied for tickets.