"There were Vietnamese believed to be among 39 migrants who were found dead in a lorry in Essex," Efe news quoted Vietnamese Foreign Minister Pham Binh Minh as saying in a tweet.
"With deepest sorrows, I would like to extend deep sympathy with and sincere condolences to families of the victims," he said, adding his government would continue working closely with the UK authorities.
Initially, police in Essex said the victims, 31 men and eight women, were Chinese, but a number of Vietnamese families have described how they fear their loved ones are among the dead.
Spokesperson of the Vietnam Foreign Ministry Le Thi Thu Hang said the authorities of the two countries have been closely collaborating to verify the identity of "the victims suspected of being Vietnamese nationals".
She said they would publish the findings "as soon as possible".
"Vietnam strongly condemns human trafficking and considers it a serious crime subject to strict penalties. Vietnam calls upon countries in the region and around the world to step up cooperation in combating human trafficking to prevent the recurrence of such (a) tragedy," she added.
Vietnamese authorities have detained four people in relation to an operation against human trafficking after the death of the migrants.
The victims were largely believed to be from Ha Tinh and Nghe An provinces.
Vietnamese migrants using irregular channels to travel to Europe can pay up to $40,000 for the journey, anti-trafficking groups have said.
( With inputs from IANS )