Rio de Janeiro is entering a period of “great hardship” in which thousands of lives could be lost, its top health official has warned, as Brazil’s president faced growing calls to change tack on coronavirus.

Jair Bolsonaro has sabotaged efforts to impose effective social distancing measures by flouting his own health ministry’s recommendations, sacking his health minister and attacking Covid-19 “hysteria”.

Asked about the rising death toll this week, the far-right populist sparked outrage by declaring: “So what?”

But on Thursday Edmar Santos, the health secretary of Rio, Brazil’s third most populous state, said an intensification of containment measures – perhaps including some form of China-style lockdown – was the only way to avoid a dramatic surge in fatalities and social turmoil.

“We are going to live through moments of great national hardship, the likes of which we’ve never experienced before,” Santos told the television network Globo.

“We aren’t a country that has lived through major wars like countries in Europe. But we’ve all lost loved ones at some point. We’re going to experience big emotional problems, social problems in the coming days and, unfortunately, we’re going to see a big rise in the number of deaths.”

According to official figures Covid-19 has so far claimed 5,466 lives in Brazil – 794 of them in Rio and 2,247 in neighbouring São Paulo.

Santos said that if current trends continued about 1,800 people would die in Rio during May – although the number would “undoubtedly be higher” if authorities failed to slow the rate of transmission.

But the secretary – who was himself diagnosed with Covid-19 earlier this month – admitted underreporting meant official figures did not capture the scale of the crisis. He believed Rio – which has a population of 17 million - actually had about 140,000 cases – more than 15 times the official number of under 9,000.

A study published in the O Globo newspaper suggested the national figures were being similarly underestimated, with more than 1.2m likely infections, compared with the official figure of under 74,000. That would mean Brazil had more cases than the United States, so far the country worst hit by the pandemic, which has about 1 million.

“The truth is this: if we don’t flatten the curve we will face chaos in May [and] a second round of chaos in June,” Santos warned, pointing to Italy, which suffered nearly 1,000 deaths on its most deadly day, in late March.

In another interview Rio’s health chief said: “What we expect for the next three to four weeks is that Rio de Janeiro and Brazil will experience the same kind of collapse that Italy, Spain and the United States have seen.”

The warnings came amid growing signs that efforts to keep Brazilians at home were faltering and with Brazil’s president facing mounting pressure to change his anti-scientific stance towards the pandemic.

Flávio Dino, the leftist governor of Maranhão state, urged Bolsonaro to make an immediate address to the nation instructing citizens to remain at home.

“Today we are at the cliff edge, on the cusp of total collapse which we need to avoid – and Bolsonaro is the main person responsible for avoiding this situation,” Dino told the news website UOL.

Sérgio Moro, the popular justice minister who abandoned Bolsonaro’s government last week, tweeted: “Unfortunately, the number of coronavirus victims in Brazil is rising sharply. It is unclear how the pandemic will evolve. Take care!”

The mayor of the crisis-stricken city of Manaus – where an average of 100 burials are being conducted each day – urged fellow mayors and governors to do what he admitted he had failed to do – convince people to stay at home.

“What I can say to them is to insist on social isolation … We have to achieve this and reach a percentage [of isolation] that causes the curve to fall,” Arthur Virgílio told the Guardian.

Virgílio accused Bolsonaro of offering Brazil’s 211 million citizens a false and dangerous choice between “freedom” and “the prison” of social isolation.

“He is offering freedom, but it is a false freedom that could represent a kind of genocide … It’s obvious that this is not going to end well,” Virgílio said.