Brazil's death toll for the Covid-19 coronavirus has overtaken that of Italy, while Mexico has reported a record number of new cases.
The increases came even as regional leaders in Latin America pushed to end quarantine measures and kick their economies back into gear.
Latin America as a whole has become a new focus of the coronavirus pandemic, with health officials urging governments there not to open their economies too fast and to avoid public crowds.
Brazil posted a record number of daily deaths for third consecutive day on Thursday local time, with 1437 deaths over 24 hours and 30,925 additional coronavirus cases, according to data released by the Health Ministry.
That brought total deaths in South America's largest nation to 34,021, trailing only the United States and the United Kingdom.
Meanwhile, Mexico reported 816 deaths on Thursday, the second consecutive daily record there, while total deaths surpassed 12,000.
Brazilian President Jair Bolsonaro has played down the pandemic since it began, criticizing distancing rules and urging regional governments to lift restrictions for the sake of the economy.
On Tuesday, he told Brazilians that death was "everyone's destiny".
Mexican President Andres Manuel Lopez Obrador also urged his country not to over-react, warning of "psychosis" on Thursday, and noting that deaths per capita for its nearly 130 million people was still far lower than in many other countries.
Mexico's deaths from the virus ranks it seventh among countries worldwide, according to the Johns Hopkins Center for Systems Science and Engineering.
With much of Latin America's population living day to day from earnings in the informal sector, many regional leaders are keen to reopen local economies, amid signs of growing hunger and strains on public finances.
The mayor of Rio de Janeiro - Brazil's second largest city, home to nearly 7 million people - allowed more than 10,000 street vendors to go back to work on Thursday
"The other day, some kid told me 'I prefer to die of coronavirus than see my family die of hunger'," Rio Mayor Marcelo Crivella told journalists.
Later in the day, during a Facebook Live session, Bolsonaro encouraged the federal solicitor general to sue states to force them into reopening their beaches.
In Brazil, health officials said there were indications new hospitalizations were stabilizing, but new deaths and confirmed cases were still growing rapidly.
Many epidemiologists warned the reopenings could be premature.