Fr Anthony Dang Huu Nam, a Catholic priest in Nghe An province, says the victims are from a rural village called Yen Thanh.
He claimed to have heard that those found dead in Essex were part of a group of more than 100 people travelling to Europe.
He told the BBC: "According to a few sources that have told me, in this case they were many people, more than 100 were on their way to a new life, but 39 died.
"A few families confirmed the deaths of their relatives who are the victims of this tragic journey."
Fr Anthony, who has among those who have led efforts to gather contact details for all the families involved in the tragedy, led prayers all day on Saturday for the situation.
"The whole district is covered in sorrow," he told Reuters news agency. "This is a catastrophe for our community."
Experts have said Vietnamese families are paying smugglers large sums of money to help transport relatives into Europe via Russia.
Bernie Gravett, a former Metropolitan police officer who now advises the EU on human trafficking, said migrants from Vietnam often enter Europe via a different route to people coming from China - the country of origin police previously identified for the container victims.
He told BBC Breakfast: "The Chinese would generally come down through Afghanistan, Kazakhstan, Turkmenistan, across through Turkey and then up what we call the Balkan route.
"With Vietnamese it's very different, they take a northern route, so generally the victims I've dealt with in the past are flown to Moscow and then they take a land route across northern Europe and then come down from there."
Gravett likened the activities of people traffickers to the operations of the Amazon website, with their network made up of "a host of resellers" working together.
He added: "When we get to Europe then they're looking [at] how can we cross Europe easily.
"So they use a European-registered truck, European drivers, so they're less likely to get stopped."
Mr Gravett said families trying to help their loved ones travel abroad would pay thousands of dollars to trafficking gangs.
He said: "In Vietnam it is assessed at 20 to 30,000 US dollars, from China it's 40 to 50,000 US dollars."
Fr Anthony said time will tell whether the tragedy will deter people in Vietnam's Nghe An province from making the risky journey to a better life in Europe.
Meanwhile, it's been revealed a 19-year-old Vietnamese woman is feared to be among the victims.
Truck driver Maurice Robinson, 25, who is known as Mo, is due to appear at Chelmsford Magistrates' Court on Monday after he was charged with 39 counts of manslaughter, conspiracy to traffic people, conspiracy to assist unlawful immigration and money laundering.
The mother and a sister of 19-year-old Bui Thi Nhung set up an alter in the village of Yen Thanh in north-central Vietnam after a family friend in the UK told them she had died after paying thousands of pounds in the hope of finding work in a nail bar.
Relatives of 26-year-old Pham Tra My told the BBC they have not been able to contact her since she sent a text on Tuesday night saying she was suffocating.
"I am really, really sorry, Mum and Dad, my trip to a foreign land has failed," she wrote.
"I am dying, I can't breathe. I love you very much Mum and Dad. I am sorry, Mother."
The woman's father, Pham Van Thin, told CNN: "The smugglers said that this was a ... safe route that people would go by aeroplane, car... if I had known she would go by this route, I would not have let her go."
Another Vietnamese father, Nguyen Dinh Gia, fears his 20-year-old son, Nguyen Dinh Luong, was among the victims.
The Vietnamese Embassy in London has started a hotline while the ambassador to the UK, Tran Ngoc An, spoke to Home Secretary Priti Patel on Friday night before meeting investigators from the National Crime Agency and Essex Police.
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