Seven members of the delegation are directly involved with Highland Park United Methodist Church, the other five people are with Texas Retina Associates.
Dr. Gary Fish, an ophthalmologist at Texas Retina Associates, his son and three technicians left Dallas on Saturday and had planned to return home Sunday.
The church reported Wednesday that all 12 members of the medical delegation were accounted for. But the church said it had differeing reports about injuries.
The family of Alexandra Paz, one of the surgical technicians, said they heard she was inside a hospital that collapsed and managed to crawl to safety.
Fish's son sent a brief text message after the earthquake saying he was OK but had lost touch with the others, Dr. Lori Coors, a colleague of the doctor, said Tuesday night.
The delegation had planned to perform free eye surgeries for poor people at a clinic in Petite Goave, a coastal town about 40 miles south of the capital of Port-Au-Prince, on Tuesday, Coors said.
Highland Park United Methodist Church has a plane on standby that can fly to Haiti to bring the delegation back to North Texas when flights resume.
There is no electricity in Port-au-Prince, United Nations humanitarian spokeswoman Elisabeth Byrs said, adding that the airport was open but not connected by a serviceable road to the city.
Early airlifts to Haiti will concentrate on search and rescue efforts, setting up makeshift hospitals and delivering food, aid officials said.
The 7.0-magnitude earthquake is being called the strongest to hit the region in 200 years. The area also saw powerful aftershocks, including several Wednesday.
Aid officials in the impoverished Caribbean nation worked Wednesday to clear rubble from roads, build makeshift hospitals and remove bodies from the rubble despite transportation problems and broken phone lines.
Humanitarian officials said the proximity of the quake's epicenter, only 10 miles (15 kilometers) from Port-au-Prince's sprawling slums and hilltop villas, as well as Haiti's crumbling infrastructure, meant it was difficult to estimate how many people might be dead or injured.
The International Red Cross said a third of the country's 9 million people may need emergency aid, but it could take days for a clear picture of the damage to emerge.
"There are many, many people trapped in the rubble," said Paul Conneally, spokesman for the International Federation of Red Cross and Red Crescent societies. "We're not optimistic at the moment."
The Red Cross said Haiti's disaster relief teams were "completely overwhelmed."
Get More: MSNBC
Randy McIlwain contributed to this report.