Latin America has suffered more than 2.5m murders since the start of this century and is facing an acute public security crisis that demands urgent and innovative solutions, a new report warns.

“The sheer dimensions of homicidal violence are breathtaking,” says the report by the Igarapé Institute, a Brazil-based thinktank focused on security and development issues.

The publication, released on Thursday, paints a bleak portrait of what it calls the world’s most homicidal continent.

Latin America suffers 33% of the world’s homicides despite having only 8% of its population. One-quarter of all global homicides are concentrated in four countries – Brazil, Colombia, Mexico and Venezuela – all of which are gearing up for presidential elections in which security is a dominant theme.

“The overall trend right now in Latin America is one of increasing homicides and deteriorating security,” said Robert Muggah, one of the report’s authors.

“Latin America is a large area and there are lots of variations. But as a region – including Mexico down to Central America and South America – the rate of homicide is set to continue increasing up until 2030. The only other places we are seeing similar kinds of increases are in parts of southern and central Africa and some war zones.”

The report lays bare how young Latin Americans are disproportionately affected, with nearly half of all homicide victims aged 15–29. It also denounces the “astonishingly” large role of guns.

Muggah said: “In addition to having these exceedingly high, epidemic levels of homicide, the vast majority of these homicides are committed with firearms. Over 75% of homicides are gun-related.” The global average is about 40%.

The security crisis has taken centre stage this year as the region’s most violent nations head to the polls. Colombia and Venezuela are both due to hold presidential elections in late May while Mexico, which last year saw its highest murder rate since records began, votes on 1 July and Brazil in October.

Seeking to exploit public anger over insecurity and crime, some candidates are floating radical responses. On Sunday, one Mexican presidential hopeful, Jaime Rodríguez, suggested chopping off thieves’ hands. “It’s a serious proposal, not something I’ve just pulled out of my sleeve,” he later claimed.

In Brazil, far-right candidate Jair Bolsonaro, an early presidential frontrunner, has vowed to relax gun-control laws. “We must give everyone the right to carry a gun, just like in the US,” he told O Globo this week. “We already have a ‘bang-bang’ going on in Brazil but only one side is allowed to shoot.”

Muggah said he feared many voters would look to strongman-style populists peddling “simple, forceful and aggressive solutions to what they see as one of their primary problems”.

“There is a risk right now that Latin Americans are seduced by this narrative of mano dura [iron fist]. [But] we will not solve this problem … by simply throwing more police, longer sentences and more prisons at it.”