The statement concluded: "Lastly, I want to thank everyone for the outpouring of support and love that we have received during this incredibly hard time".
Shortly after he was shot, Ortiz was taken to Abel Gonzalez Center for Advanced Medicine in Santo Domingo, where he underwent his first surgery.
Dominican police said that 25-year-old Eddy Feliz Garcia got off a motorcycle and shot Ortiz in the back while Ortiz was at the Dial Bar and Lounge in Santo Domingo Sunday evening.
Former Red Sox catcher Jason Varitek becomes emotional talking about David Ortiz and is very complimentary of his former teammate.
Ortiz has been alert, has spoken to his family and "even flashed that smile", his media assistant, Leo Lopez, told ESPN.
There's no denying David Ortiz left a big impact on a lot of people.
Two other people were injured during the ambush, including television presenter Jhoel López; police said they were investigating whether Ortiz was the intended target. One of the men shot a single bullet into Ortiz as the patrons ran for cover. He was treated at a local hospital before being released into police custody.
Ortiz retired from baseball following the 2016 season. "We as for privacy as David works towards recovery". His postseason heroics helped Boston capture its first World Series title in 86 years in 2004, when he was the Most Valuable Player of the American League Championship Series as the Red Sox overcame a 3-0 series deficit to the New York Yankees in seven games.
The Red Sox icon underwent surgery in the D.R. and was transported to Boston on Monday, where he again underwent surgery.
The Red Sox arranged for an air ambulance to transport Ortiz from the Dominican Republic to Boston.
He had helped rally the city after the Boston Marathon bombings that year, giving a speech at Fenway Park, telling the crowd to stay "Boston strong". He maintains a home in Weston, on the outskirts of Boston.