At least 22 of the dead worked with the American International Assurance Co., the building's largest tenant, a company official said. More than five other employees were missing, he said.
The International Trade Center building housed the disco along with two floors of shops, 50 offices and a a restaurant where about 120 people were attending a wedding reception.
Police were investigating whether cutting torches used by the welders triggered the fire, which started Tuesday afternoon and burned for at least five hours, city officials said.
Police were also investigating the possibility of a gas leak, they said.
The confirmed death toll rose to 61 but the toll could rise with scores of people still hospitalized, many with critical injuries.
The dead included two Britons, a Vietnamese-American, and a Croatian, city officials said.
About 100 agents for American International Assurance were undergoing training in the building when the fire - worst in the city's history - broke out.
Huynh Thi Mat, an agent who jumped to safety, said people panicked when the electricity went out and smoke poured up the stairs.
``We rushed to the roof, and I started climbing down a rain water drainage pipe outside the building. At first I didn't dare jump from there, but I realized if I didn't I could be killed by the fire. I'm lucky, because many people could not escape. I broke my leg.''
