In Venezuela, a monthlong national lockdown has led to a reduction in homicides and other violent crime, but has also been accompanied by a surge in extrajudicial killings by government security forces, said Roberto Briceno León, head of Venezuelan Violence Observatory, a nonprofit monitoring group.

“The delinquents have retreated and the police have carried on their operations,” Mr. Briceno León said.

And the crime-fighting benefits of the lockdowns have barely started to register in Mexico, a nation with a highly complex criminal landscape. In March, the government recorded 2,585 homicides, one of the highest monthly totals on record.

But the administration of President Andrés Manuel López Obrador had also been slower than many other countries in the region to impose measures to combat the spread of the virus. His government waited until late March to issue stay-at-home orders and also made them voluntary. In some neighborhoods of the nation’s largest cities, life has continued more or less as normal.

Still, there is evidence that the measures have begun to put a dent in Mexican crime.

Maribel Cervantes Guerrero, the secretary of public security for the state of Mexico, the country’s largest state, said that since the government launched its stay-at-home campaign, officials have seen a decrease in most crimes, including homicides, which fell to 42 last week from 74 the week prior.