During an inspection of the quake damage earlier this week, he said he was "very concerned" about the Morelos complex, where each structure houses 54 apartments.
Gonzalez admitted that she shared some of that concern.
"They told me we were in no danger, but they warned us the decision to stay was our own responsibility," she said.
The death toll from the quake has been rising steadily and now stands at 293
Ryan Callahan Salute to Service Jersey
, with most registered in densely populated Mexico City, said the national civil protection agency on Friday.
Rescue workers are continuing to search for survivors.