"I'm very sorry, I made a mistake. It won't happen again," the king said as he left a Madrid hospital where he was treated for a hip injury suffered during the Botswana trip, the BBC reported.
The palace refused to comment on reports that he went to Botswana to hunt elephants.
The 74-year-old king is honorary president of the Spanish branch of the World Wildlife Fund.
An online petition calling for his resignation from that post accumulated 85,000 signatures before his apology.
The king was rushed back to Madrid after he fractured his hip during a fall and had surgery Saturday, CNN reported.
Notable deaths of 2014 [PHOTOS]