Tregre said someone called deputies with a description of a car fleeing the scene, and officers tracked it to a nearby trailer park.
When officers found the car, they handcuffed a suspect outside a trailer, then knocked on its door. Tregre said someone with a dog answered.
"Another person exited that trailer with an assault weapon and ambushed my two officers," Tregre said. Two deputies were killed and a third was wounded.
Two suspects were wounded in the shootout before officers subdued them, Tregre said.
The dead deputies were identified as Brandon Nielsen, 34, and Jeremy Triche, 27. The wounded officers were Jason Triche, 30, and Michael Boyington, 33. They were being treated at area hospitals but the extent of their injuries was not known. The Triches are not believed to be related.
The suspects were not immediately identified.
The initial shooting occurred around 5:30 a.m. at a parking lot off Louisiana Highway 3217 used by workers in the industrial area about 20 miles west of New Orleans, near the line between St. Charles and St. John the Baptist parishes. A massive grain port also is nearby. There is heavy traffic in the area as shifts change at plants and port facilities.
Bill Day, spokesman for Valero Energy Corp., said one of the deputies was providing security for an off-site parking lot used by contractors working at the Valero St. Charles Refinery.
Day said operations at the refinery had not been affected. Valero employees were being asked to report to work as normal, unless they park at the lot where the incident took place.
Some other plants in the area were letting non-essential workers in the area leave for the day or were telling them not to report for work as the search continued.
Police officers from throughout metro New Orleans rushed to the scene after the shootings in anticipation of a possible manhunt.
Tregre said an active search for suspects was no longer under way. State police are taking over the investigation.