There were 2,409 new virus confirmations, the first time that number has exceeded 2,000 in one day. In percentage terms, at 6%, it was not the largest one-day percentage rise.
"We are at the moment of the fastest growth in new cases," Assistant Health Secretary Hugo López-Gatell said, calling it "the peak moment."
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"This is the most difficult moment," he added, though he also said there were "tendencies of decline" in cities like Cancún, Villahermosa in the Gulf coast state of Tabasco, Culiacán in the northern state of Sinaloa, and the border city of Tijuana.
Officials also reported 257 more deaths from COVID-19, for a total of 4,477 since the pandemic began. There have been higher one-day death tolls this week.
The increase in cases came just four days before Monday's scheduled partial re-opening of key industries such as mining, construction and automobile assembly. López-Gatell has stressed that the re-opening of those industries will be largely preparatory, with a broader restart of businesses and other activities not occurring until June 1.
There were signs that hospital capacity was nearing its limit in Mexico City, the hardest-hit area. The Health Department reported that 73% of the capital's general-care hospital beds were full. The percentage was lower for intensive-care beds, partly because of the expansion of improvised ICU units at hospitals and other venues.