"You could say that 30 years ago they probably would have raced in these conditions, but safety has come a long way in terms of the circuits and the way that we view safety," said McLaren's Jenson Button.
It means the grid will only now be decided after the session resumes at 11am on Sunday, just six hours before the world championship begins in the twilight timeslot, 5pm.
"We'll have to follow a really tight schedule tomorrow, including a very short turnaround between qualifying and race, and that'll be tough for everyone," added Button's teammate, Sergio Perez.
The possibility of More rain - albeit probably lighter than Saturday's - is forecast for Sunday.
Red Bull team boss Christian Horner backed the FIA's decision to delay qualifying in the fading daylight.
"Hopefully this weather will blow through tonight and we'll be back with better conditions in the morning," he said.