Mexico on Thursday passed the grim milestone of 50,000 coronavirus deaths, far more than the worst-case estimates of the government, which faces criticism of its handling of the crisis and the economic fallout.

The country has the world's third-highest fatality toll from the disease, behind only the United States and Brazil.

The health ministry announced 819 more deaths in its daily update, taking the total to 50,517 since the Latin American nation's first case was detected in February.

The overall number of infections registered now stands at 462,690 in the nation of more than 128 million.

"Unfortunately, because it is always unfortunate even if it was only one, we have 50,517 deaths from COVID-19 in Mexico," deputy health minister Hugo Lopez-Gatell told a news conference.

When it comes to deaths per 100,000 inhabitants, Mexico is in 13th place worldwide, based on official data.

The death toll far exceeds the range of between 6,000 and 30,000 projected by the government of President Andres Manuel Lopez Obrador in February.

Those estimates soon began to look implausible as Mexico, where self-isolating to stop the virus spreading was voluntary, began to gradually open up parts of its economy.

Although the death toll continues to rise, Lopez-Gatell, who oversees the fight against the virus, voiced optimism this week that there was already "better control".

The epidemic is still active, "but during the month of July it began to slow down," he said.

Some experts question the government's performance in confronting the crisis.

"The number of cases, like deaths, must be substantially more than official figures show since we have done few tests," Alejandro Macias, who led the country's fight against the swine flu pandemic in 2009, told AFP.

At the same time, he acknowledged successes such as revamping hospitals to deal with the crisis.

But in other areas, such as the number of tests carried out, "Mexico has frankly gone against international recommendations," Macias said.

The government maintains that the health system has suffered from neglect stretching back three decades, long before it came to power, resulting in a shortage of 240,000 professionals.

It says there is no conclusive evidence that mass testing is an effective way of controlling the virus.

The government has also been criticized for not doing more to promote the use of face masks.

"I don't think it has been recommended enough at the federal level," Macias said.

Lopez Obrador had never been seen wearing a mask until he flew to the United States last month to meet President Donald Trump, although his public activity is very limited.

Lopez-Gatell, his coronavirus czar, has called for the use of masks, while telling Mexicans that it is not enough unless complemented by hygiene and social distancing measures.