The suspect, Tyrone Williams, 35, pleaded not guilty in the case, which stems from a May 13, 2003 tragedy in which the Jamaican truck driver transported 85 immigrants in his closed truck in the sweltering desert heat.
Williams could face the first US death sentence in a human smuggling deaths case if convicted.
The jury at the first trial, which took place in March 2005, while convicting Williams on some counts, could not agree on whether he bore direct responsibility for the deaths and deadlocked on some charges, prompting prosecutors to retry the case.
The 19 victims died of overheating, dehydration and suffocation when the temperatures rose in the trailer, which lacked air conditioning, and air became scarce.
Prosecutor Daniel Rodriguez in opening remarks described the vehicle as a "death chamber" and portrayed Williams as devoid of remorse or sense of guilt.
Defence attorney Craig Washington insisted that Williams never knew exactly how many people were being transported in the closed truck, and blamed another man in the smuggling ring for the deaths.

Copyright AFP (Agence France-Presse), 2006