Four are in a "very serious" condition, with another listed as "serious", Spanish media reported. But five of six people classed as "serious" overnight have shown signs of improvement, the Efe news agency said.
Eight remain under observation with one only slightly injured, Spanish media said.
The worst is the identification of the bodies. It is the end of all hope
The body of a baby and an adult, the two final victims of the crash, were pulled from the burnt-out wreckage of the plane on Thursday.
Two babies and 20 children were on board the flight, which was heading from Madrid to Las Palmas in the Canary Islands, according to Spanair, which released the official passenger manifest.
Spanair bosses expressed their shock and sadness at the crash, telling a news conference in Madrid that the focus of their energies would now be on helping the survivors and the relatives of those killed.
Spanair and its Scandinavian owner, SAS, were putting "all resources" into supporting those affected by the disaster, Spanair chief Marcus Hedblom said.
"We are committed to continue to give that support for a long, long time from now," he added.
At a temporary mortuary at a conference centre close to Madrid's Barajas airport, emotions among those waiting for confirmation of their loss were running high.
The BBC's Steve Kingstone, in Madrid, says many of the relatives have expressed anger and disgust at Spanair, blaming the company for the accident.
The injured include a young brother and sister, who immediately asked rescue workers about their parents, our correspondent adds.
Examination of the wreckage began the morning after the crash
Experts say work to identify the dead is likely to be slow and painstaking, as many of the bodies were badly burnt in Wednesday's inferno.
El Mundo newspaper reported that 38 corpses had been identified by Thursday afternoon, with a team of 40 forensic analysts expected to complete the rest of the identifications within 48 hours.
"The worst is the identification of the bodies," Red Cross spokesman Jesus Lopez Santana told the El Mundo newspaper.
"It is the end of all hope and [it is] when we see the worst scenes, because the majority of the relatives break down when they hear the news."
The Spanair flight, bound for Las Palmas in the Canary Islands, took off on Wednesday at lunchtime with 172 people on board, among them 10 crew.
The MD82 is known as a versatile and reliable aircraft
Initial reports suggested a fire had broken out in one of the MD82 plane's engines during or shortly after take-off, and the plane ended up in a field.
Spanish Transport Minister Magdalena Alvarez said the plane had earlier begun taxiing to the runway, before turning back because of a technical problem, which had caused an hour's delay in take-off.
Spanish media said the pilots had reported a fault with a temperature gauge, but it was thought to have been fixed before take-off.
Speaking on Thursday, Ms Alvarez said a thorough investigation would be carried out, with a full examination of the flight recorders and available pictures, but that it was very early to draw conclusions about the crash.
A special independent commission has been established to investigate the cause of the crash, Spanish media reported.
The plane which crashed was a 15-year-old McDonnell Douglas MD82 plane previously owned and operated by Korean Air.
Reports said it was serviced regularly and had been pronounced fit to fly.
The MD82 is known as a versatile and reliable aircraft, with some 432 planes currently in service around the world, Spain's EFE news agency said.
People concerned for relatives or friends who might have been on board the plane can call Spanair's helpline on +34 800 400 200 (calls possible from inside Spain only).
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