More than 600 schools have now been surveyed for collapse-risk concrete, senior officials in the Department for Education have said.
Officials also confirmed that the department has received 98% of responses to a questionnaire about potential reinforced autoclaved aerated concrete (Raac) in their buildings.
It comes after ministers set a deadline of last Friday for school leaders and responsible bodies to respond.
The new figures emerged as permanent secretary at Department for Education Susan Acland-Hood and chief operating officer Jane Cunliffe appeared before the Public Accounts Committee (Pac).
The two top officials were grilled by MPs about the ongoing crisis, with Pac chair Dame Meg Hillier telling the civil servants that it was “disappointing” the pair had not come before MPs ready to provide more figures.
The Department for Education officials resisted questions about how many schools were waiting for a survey for Raac, amid questions from Dame Meg about whether the number was in the “tens” or “hundreds”.
Ms Cunliffe said: “It is very fast-moving, we are doing tens of surveys every day.”
She said that eight surveying firms were currently doing both new and return visits to schools.
“As soon as we hear about a school that suspects it has got Raac, we can get that survey done in weeks. So we are hoping over the next few weeks, to have identified the majority.”