The 20 families expecting to move into the newly built Treadmark building in Dorchester were within weeks of realizing the dream of living in bright new affordable housing in a vibrant neighborhood with easy access to public transportation.

But the six-alarm fire that ripped through the mostly wood structure Wednesday — just a day before city officials were to make a final inspection — put that dream on hold.

The Boston-based developer, Trinity Financial, had conducted a lottery to determine who would be the building’s new residents and Thursday the company vowed to rebuild and to honor the commitment to those who had won that lottery.

“We are committed to rebuilding as quickly as possible,’’ said Jim Keefe, principal at Trinity. “Now that the fire is out, our primary mission is to redouble our efforts to fulfill our promise of providing long-term affordable housing.’’

How long it will take to rebuild the six-floor building in the Ashmont section of Dorchester was unknown Thursday, but city officials said the 20 families seem well situated to wait.

“It is our understanding that all 20 families are currently in safe, stable housing situations that can be extended,’’ said Sheila Dillon, the city of Boston’s housing chief.

Trinity had planned a total of 51 rental units in the Treadmark, all for tenants with incomes significantly below area median income.

Besides the 20 families already qualified on income level and on background checks, dozens more had won the lottery. They too will keep their places in the line for the Treadmark.

“Trinity will be reaching out to those households who had high lottery numbers but had not yet received units, and is working with the Office of Fair Housing to outline a process by which those households will retain their lottery positions,’’ Dillon said.

Trinity also planned to sell 28 market-rate condominiums and four affordable ones. Most of those people had purchase-and-sale agreements signed with the developer, which meant they were committed to buying their units and had put down sizeable deposits.

The cause of the fire was still under investigation Thursday, but if any evidence of negligence is found, those prospective buyers with purchase-and-sales agreements may be in a position to seek damages, such as for expenses incurred in getting alternative housing temporarily, according to Martin W. Healy, chief legal counsel for the Massachusetts Bar Association.

“It’s a potential avenue,’’ he said.

If no one is found responsible for the fire, the prospective buyers will have to bear any extra expenses, he said.

Fire Commissioner Joseph Finn and Inspectional Services Commissioner William Christopher Jr. said the building was so close to being occupied that the “life/safety’’ inspections were scheduled to be conducted Thursday. The building had received the proper permits and had a sprinkler system installed as required by state building code, they said.

“It’s a sad set of circumstances,’’ Finn said.

However, Finn said, it was not clear if the sprinkler system was functioning Wednesday when the fire started on the sixth floor and made its way into a 1-foot void between the ceiling and the roof, where it strengthened and frustrated firefighters’ efforts to quell it.

He said sprinklers were installed in the void, but they did not function during the fire.

“They were not functioning. Was it offline? How did it fail? Was it shut down?’’ Finn said. “It’s all going to be determined. It’s all in the investigatory phase.’’

The fire inside the void space was so intense, he said, that firefighters were ordered off the roof and out of the building within nine minutes of their arrival by commanders who feared that heavy air-conditioning equipment at the top of the building would plunge through.

The building used a construction technique in which the upper floors are framed in wood based on a platform of concrete and steel, a practice in extensive use in Boston as contractors look to trim costs and increase the number of units they can create in apartment buildings, the Globe reported Thursday.

Finn said the wood framing provided fuel for the fire, but he also stressed that the use of wood framing is not a safety risk — provided smoke alarms and sprinkler systems are fully functional.

The $45 million Treadmark project was being built with the help of about $10 million in city, state, and federal subsidies. That funding enabled the developer to offer most of its 83 apartments and condos at prices affordable to lower- and middle-income residents.

Sean P. Murphy can be reached at smurphy@globe.com. John R. Ellement can be reached at ellement@globe.com. Emily Sweeney can be reached at esweeney@globe.com.