The aircraft's captain, two passengers and a motorist, believed to be a taxi driver, were killed.
TACA airline president Alfredo Schildknecht said the Airbus A320 skidded off the runway after the pilot made a second attempt to land in heavy rain and fog.
"We know there was bad weather at the moment of the landing and the captain was not able to land in his first attempt," he told a news conference.
"He landed in the second attempt, apparently braking conditions were not optimum, the landing strip was wet and the plane [skidded] off at the end of the runway."
A doctor at the hospital treating the injured named one of the dead passengers as Harry Brautigam, director of a regional development bank.
Jeanne Chantal Neele, wife of Brazilian Ambassador Brian Michael Fraser Neele, is reported to have died in the crash, and the former head of Honduras' armed forces, Gen Daniel Lopez Carballo, is said to be among the injured.
One survivor, Mario Castillo, described the crash on Honduran TV: "Suddenly we felt a big noise and we were all trying desperately to get out.
"The worst injured were the people in business class."
Authorities hosed down cars trapped beneath the wreckage, and tried to clear away hundreds of onlookers amid fears of an explosion or fire.
The flight, which originated in Los Angeles, left San Salvador at 1430 GMT.
It had been scheduled to stop briefly in Tegucigalpa and in San Pedro Sula before heading to Miami, Florida.
Tegucigalpa, surrounded by hills, is one of the most difficult airports in the region for landing because of its short runway and an unusually steep approach.
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