He added: "Our priority has been to identify the victims, to preserve the dignity of those who have died and to support the victims' friends and families".
The British and Vietnamese authorities are now working to repatriate the bodies.
Essex Police said it only released the names after an exhaustive operation to ID them all and alert next of kin, with DNA samples sought from many relatives in Vietnam to confirm identities.
Ten teenagers, including two 15-year-old boys, were among the victims whose bodies were found on October 23 in a container in the southeastern British region of Essex.More news: Rep. Nunes Demands Adam Schiff Testify in Impeachment Inquiry
Following confirmation that the truck victims were Vietnamese, Vietnam's Prime Minister Nguyen Xuan Phuc sent a letter of condolence to the families of the victims on Thursday. "Vietnam calls upon countries in the region and around the world to step up cooperation in combating human trafficking in order to prevent the recurrence of such tragedy".
On October 23, United Kingdom emergency services discovered the bodies of 39 people in a refrigerated container truck at the Waterglade Industrial Park in Grays, Essex County, east of London. Police said the truck and the container entered the country at two separate times.
The victims came from six provinces - Haiphong, Hai Duong, Nghe An, Ha Tinh, Quang Binh and Hue - Vietnam's Ministry of Public Security said in a statement.
The container was picked up at Purfleet dock, east of London and police originally said the victims were believed to be Chinese.More news: United Kingdom backpacker was strangled by Tinder date
Among the victims was Pham Thi Tra My, 26, from a village in Ha Tinh, Vietnam, who had texted his mother hours before the bodies were discovered: "I'm sorry, mom, my way to foreigner did not succeed". "Mom, I love you and dad very much".
The truck driver Maurice Robinson, 25, of Craigavon, Northern Ireland, was charged with 39 counts of manslaughter, conspiracy to traffic people and money laundering.
People traffickers charge up to £30,000 per person for those seeking a better life to be smuggled overseas.
They are also in the process of extraditing another suspect from Ireland and searching for others potentially involved.Vietnam has held 11 people in connection with the deaths for helping people travel abroad with the intention of staying overseas illegally.More news: Valverde accepts Barca under pressure after Slavia stalemate