As he did so, the monarch addressed the controversy surrounding his recent trip to Botswana.
It followed days of headlines about the private visit reportedly to hunt elephants, which is legal to cull herd numbers.
The king, who is president of the Spanish branch of the World Wildlife Foundation, said: "I'm sorry. I made a mistake. It won't happen again".
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Eyebrows were raised over the expensive trip, particularly since the sovereign made a speech two weeks ago voicing concern over his country's economic crisis.
In Wednesday's brief but unprecedented statement to the cameras Juan Carlos I looked sombre and contrite.
Leaning on crutches, the king also said that he was looking forward to getting back to his duties - he has a meeting on Friday with Prime Minister Mariano Rajoy.
The 74-year-old, who seemed fragile, thanked the medical team for their care.
Until this incident the head of state had enjoyed enduring popularity with the Spanish public, especially given his decisive role in thwarting a coup in the early years of the democracy.
This has been one of the most difficult weeks of his 36-year reign.
The hunting expedition came to light after he fell down a flight of stairs and had to be flown back by private jet.
His accident comes just after his 13-year-old grandson had to be treated in hospital for accidently shooting himself in the foot.
In the last year the royals have also been hit by a corruption investigation into the business affairs of the king's son-in-law Iñaki Urdangarin.
Facing these difficulties, the family have rallied around their partriarch. His heir Prince Felipe visited him with his wife and daughters and has stepped in to cover official business.
His wife Queen Sofia travelled back from a trip to see relatives in her native Greece on Monday.
The couple will celebrate their 50th wedding anniversary in May.