His son Ben Ford tweeted Saturday, thanking fans for their concern and saying Ford, 72, has "the best care possible."
Ford's publicist, Ina Treciokas, has described the actor's injuries as non-life-threatening. He remained hospitalized Sunday.
Ford reported engine trouble shortly after taking off from the Santa Monica Municipal Airport on Thursday and asked for an immediate return, said National Transportation Safety Board investigator Patrick Jones. The tower then reported that the plane came up short of the runway, according to air traffic controller transmissions from LiveATC.net.
Ford appeared to do "his best to keep the airplane flying," according to ABC News consultant Col. Stephen Ganyard.
"It looks like he did a really good job under the circumstances," Ganyard added.