The tech tycoon made the shock allegations after 63-year-old Vern Unsworth dismissed his offer of donating a mini-submarine to the rescue effort as a “PR stunt”.
In response Mr Musk, 47, posted a series of tweets and referred to the British caver as “pedo guy”, apparently on the basis that he is a western man living in Asia.
But after coming under pressure from investors his his tech firms he returned to social media to post an apology.
He said: “His actions against me do not justify my actions against him, and for that I apologise to Mr Unsworth and to the companies I represent as leader.
“The fault is mine and mine alone.”
The billionaire added his words were “spoken in anger”.
Mr Unsworth said he was “astonished and very angry” at the Tesla co-founder’s comments and was considering taking legal action.
The row erupted after Mr Musk flew to Thailand and left his submarine at the entrance to the cave network where the 12 boys and their coach were trapped.
Thai officials thanked him for his offer but the rescuers largely ignored the vehicle, saying that it was not practical.
An unimpressed Mr Unsworth said: “It just had absolutely no chance of working. He had no conception of what the cave passage was like.
“The submarine I believe was about 5ft 6in long, rigid, so it wouldn’t have gone round corners or round any obstacles.
“It wouldn’t have made the first 50 metres into the cave from the dive start point.
“He can stick his submarine where it hurts.”
Mr Unsworth lives in Chiang Rai, northern Thailand, about 40 miles from the Tham Luang caves where the boys became trapped.
The experienced explorer is familiar with the cave network and predicted where the boys would have taken shelter.
He also helped Thai authorities get in touch with British experts who took part in the rescue.