There were 3,001 deaths in 24 hours, after a peak of more than 4,000 was reached at the start of April.
The 14-day average of deaths and cases remains high but has seen a slight fall.
Congress has opened an inquiry into the government's handling of the pandemic.
President Jair Bolsonaro, who has frequently spoken out against lockdowns, masks and defended unproved drugs as treatment, is facing widespread criticism and his support has plummeted.
