Argentina and Colombia on Wednesday announced that travellers from the countries worst-affected by the new coronavirus would be isolated to protect the wider population.
Argentina was the first country in the region to register a coronavirus-related death on Saturday, with Panama announcing another on Tuesday.
President Alberto Fernández's government has announced a two-week isolation period for people arriving from China, Italy, France, Germany, Spain, Japan, South Korea and the United States.
"This is not voluntary, it's not a recommendation. If you don't comply you'll be committing a crime, which is putting the public health at risk," Fernández told the FM Delta radio station. "The person who complies with the 14-day quarantine is obliged to shut himself away at home alone."
The Peronist leader said Argentina was considering barring travellers from Italy, the worst affected European country and one from which many Argentines are descended and where they still have family.
Argentina has registered 19 coronavirus cases and one death, a 64-year-old man who had arrived in Buenos Aires from France. In Latin America, only Brazil has registered more cases with 34.
Colombia has seen only three cases so far but also announced measures against travellers arriving from certain countries.
"Given the implications of the quarantine by China, Italy, Spain and France, the national government is adopting the preventive isolation of people coming from those countries to protect the collective health," President Iván Duque said on Twitter.
Colombia's first infection was detected in a 19-year-old woman who arrived in Bogotá on Friday from Milan.
Two more cases were confirmed on Monday – in a 34-year-old man and a 50-year-old woman, both of whom had been in Spain.
On Tuesday, Chile was the first Latin American country to announce a quarantine on arrivals from Spain and Italy, who will be placed under the surveillance of health authorities.
Worldwide, almost 120,000 coronavirus cases have been recorded in 110 countries and territories, killing more than 4,300 people.