Lopez said Ortiz underwent six hours of surgery.
Kennedy said he had been texting Ortiz's wife, Tiffany, who was in the States with their kids, and that "she expressed her gratitude" for all the support. Please know we are doing everything we can to support David and his family during this very hard period.
We have offered David's family all available resources to aid in his recovery and will continue to keep them in our hearts.
Doctors removed his gallbladder and part of his colon and intestines, and Ortiz also sustained liver damage.
The shooting unfolded Sunday night at the Dial Bar and Lounge, a nightclub in Santo Domingo, the capital of the Dominican Republic. About 10% of those players come from the Dominican Republic, including Chicago White Sox rookie Eloy Jimenez.More news: United States signed ‘another very important part’ of immigration deal with Mexico
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Police said Ortiz was shot at almost point-blank range by a man identified as Eddy Feliz Garcia, 25. The footage shows people scattering after gunfire erupted and Ortiz, who had been sitting at the outdoor bar, appear to grab his side and then collapse. Jhoel Lopez, a television host who was at the club with Ortiz, was also shot.
Police have not yet released the identity of the suspected gunman.
Police are searching for a second suspect. He was treated at the Dario Contreras Hospital in Santo Domingo before being released to police custody.
The Red Sox legend was transported from Boston's Logan Airport to Massachusetts General Hospital by ambulance with a police escort.
Former President Barack Obama, a White Sox fan, tweeted, "Get well soon, Papi", alongside a photo of him getting a personalized Red Sox shirt from the slugger when the team visited the White House in 2014.
Francona managed Ortiz with the Red Sox from 2004-11, a stretch that included two of the three World Series titles Ortiz won with Boston.
Eliezer Salvador, a friend of Ortiz's who said he drove the slugger to the hospital in the aftermath of the shooting, told The Associated Press he asked Ortiz if he knew of any enemies who would want to have him killed.