6/10 1:08 PM PT -- David Ortiz's father, Leo Ortiz, is speaking with reporters in the D.R. -- saying he wants to thank the doctors for "saving my son's life."
Leo said David WILL be transported to Boston -- and explained that David's personal doctors and his wife live in Massachusetts.
David's doctor said the surgery was successful -- noting the bullet struck the liver, the small and large intestines. He says Ortiz's gall bladder was removed to make space to treat the affected organs.
6/10 12:36 PM PT -- Boston Red Sox management just addressed the media and said Ortiz's condition is still serious following Sunday night's shooting but he's stable enough to travel back to the United States.