The aircraft - which was flying to Las Palmas in the Canary Islands, a popular holiday destination - is reported to have been attempting an emergency landing soon after lifting off when the incident happened.
Tessa Parry-Wingfield, reporting for Al Jazeera from Madrid, said on Thursday the country was in a "state of shock".
She said 153 people were confirmed dead and only 19 people survived.
"The death toll could rise sharply over the coming days and a makeshift morgue has been set up in the city centre," she said.
"Relatives have been flocking to see if their loved ones are amongst the victims. Rescue workers say it is amazing there were any survivors at all."
Investigations are under way but there are little facts yet about what happened, said Parry-Wingfield.
"What we do know is speculation and witness reports. They say an engine caught fire on take off when the plane was reaching its maximum speed. That caused the aircraft to come down, and it caught fire before crashing into the field to the side of the runway."
Parry-Wingfield said Jose Rodriguez Zapatero, Spain's prime minister, had expressed sympathy and that Spain's king and the queen were due to speak while Spanair would give a news a conference.
Clouds of smoke were seen billowing from near the runway after the crash at terminal four.
"The scene is devastating," Pablo Albella, a Madrid city rescue worker, said as crews removed bodies and injured people from the aircraft belonging to Spanish airline Spanair.
"The fuselage is destroyed. The plane burned. I have seen a kilometre of charred land and few whole pieces of the fuselage. It is all destruction."
The victims' bodies were so hot that police could barely touch them and the shattered wreckage bore no resemblance to an aircraft, one police officer told El Pais newspaper.
|Some of the survivors were said to be in critical condition [EPA]
Chris Hodgkinson, technical director of the Guild of Airpilots and Air Navigators, told Al Jazeera: "One can only assume at this time that this was due to mechanical failure."
Helicopters and fire engines pumped water onto the burning plane, which crashed into a wooded area at the end of the runway.
The aircraft's "black box" flight data recorder has been retrieved.
The plane's takeoff had been delayed by about an hour due to technical problems.
Sergio Allard, Spanair's spokesman, said the plane had passed an inspection test in January of this year and no problems with it had been reported.
The plane was 15-years-old and had been owned by Spanair for the past nine, he said.
Madrid airport cancelled departures on Wednesday and restricted the number of aircraft arriving.
Spanair, Spain's second-biggest airline after Iberia, is a subsidiary of Scandinavian carrier SAS.
The MD-80 family of twin-engine medium-range airliners enjoyed wide popularity among the world's airlines in the 1970s, 80s and 90s.
But it has had a number of fatal accidents, the worst of which was a crash of Slovenia's Adria Airways flight in Corsica in 1981, when all 180 people on board perished.
Five passengers on a Spanair flight from Spain's Basque region to Barcelona were injured in an emergency evacuation on January 9, 2006.
The airline, which has a fleet of 65 jets, was founded in 1986 and says it has since carried more than 104 million passengers from about 100 European destinations to Spain.
A member of the Star Alliance network, it recently proposed shedding almost a quarter of its 4,000 staff because of the fuel price rise crisis and reduced demand.