Rojas tweeted Monday afternoon that Dr. Abel Gonzalez, who performed the surgery, had said Ortiz was in stable enough condition to travel.
Earlier in the day, Ortiz's media assistant updated his condition.
"Doctors say he is out of danger, but he is heavily sedated and will be in intensive care for the next 24 hours," Leo Lopez told ESPN.
David Ortiz through the years
David Ortiz through the years
BOSTON, MA - MAY 22: David Ortiz #34 of the Boston Red Sox smiles as stretches before a game against the Boston Red Sox at Fenway Park on May 22, 2016 in Boston, Massachusetts. (Photo by Jim Rogash/Getty Images)
23 Feb 1998: David Ortiz #27 of the Minnesota Twins at Spring Training at the Hammond Stadium in Fort Myers, Florida. Mandatory Credit: Rick Stewart /Allsport
25 Jun 2000: David Ortiz #27 of the Minnesota Twins reacts to the action during practice before the game against the Anaheim Angels at Edison Field in Anaheim, California. The Angels defeated the Twins 7-6.Mandatory Credit: Tom Hauck /Allsport
CLEVELAND, UNITED STATES: Minnesota Twins player David Ortiz (L) sprays champagne on teammate Torii Hunter (C) while Hunter is being interviewed by an unidentified television reporter (R) in the locker room during the post game victory celebration15, September, 2002 at Jacobs Field in Cleveland, OH. Minnesota clinched the American League Central Division championship, defeating the Cleveland Indians 5-0. (Photo credit should read DAVID MAXWELL/AFP/Getty Images)
SARASOTA, FL - FEBRUARY 23: David Ortiz of the Boston Red Sox poses for a portrait during the Red Sox spring training Media Day on February 23, 2003 at Ed Smith Stadium in Sarasota, Florida. (Photo by Craig Jones/Getty Images)
BOSTON, MA - AUGUST 30: First baseman David Ortiz #34 of the Boston Red Sox watches the hit during the game against the New York Yankees at Fenway Park on August 30, 2003 in Boston, Massachusetts. The Yankees won 10-7. (Photo by Rick Stewart/Getty Images)
Designated Hitter David Ortiz (34) of the Boston Red Sox crosses home plate after crushing a home run against the Anaheim Angels at Angels Stadium on July 17, 2004. (Photo by Phillip Ellsworth/WireImage)
BOSTON - OCTOBER 18: Red Sox designated hitter David Ortiz rounds the bases and celebrates his game winning home run as he leaps across the plate. (Photo by Jim Davis/The Boston Globe via Getty Images)
BOSTON - OCTOBER 23: David Ortiz #34 of the Boston Red Sox hits a three run home run in the first inning against the St. Louis Cardinals during game one of the World Series on October 23, 2004 at Fenway Park in Boston, Massachusetts. (Photo by Ezra Shaw/Getty Images)
ST LOUIS - OCTOBER 27: (L-R) Pedro Martinez #45, Curt Schilling #38 and David Ortiz 34 of the Boston Red Sox celebrate after defeating the St. Louis Cardinals 3-0 in game four of the World Series on October 27, 2004 at Busch Stadium in St. Louis, Missouri. (Photo by Jed Jacobsohn/Getty Images)
BOSTON - OCTOBER 30: Red Sox player David Ortiz clutches the championship trophy as the rolling rally parade to celebrate the baseball team's World Series win rolls along Boylston Street. (Photo by Stan Grossfeld/The Boston Globe via Getty Images)
BOSTON - MAY 22: David Ortiz #34 of the Boston Red Sox waits on deck to hit against the Atlanta Braves at Fenway Park on May 22, 2005 in Boston, Massachusetts. The Red Sox won the game 5-2. (Photo by Scott Cunningham/Getty Images)
BOSTON - SEPTEMBER 16: David Ortiz rubs teammate Manny Ramirez's head after Ramirez was hit by a pitch in the 10th inning, walking home the winning run in the Red Sox 3-2 win over Oakland tonight. (Photo by Barry Chin/The Boston Globe via Getty Images)
HOUSTON - OCTOBER 26: Andruw Jones of the Atlanta Braves and David Ortiz of the Boston Red Sox pose with the Hank Aaron Award, presented to each before Game Four of the Major League Baseball World Series between the Chicago White Sox and the Houston Astros at Minute Maid Park on October 26, 2005 in Houston, Texas. (Photo by Brad Mangin/MLB Photos via Getty Images)
PITTSBURGH - JULY 10: Amercian League All-Star David Ortiz of the Boston Red Sox watches a second round home run during the CENTURY 21 Home Run Derby at PNC Park on July 10, 2006 in Pittsburgh, Pennsylvania. (Photo by Jamie Squire/Getty Images)
ANAHEIM, CA - AUGUST 23: David Ortiz #34 of the Boston Red Sox laughs before the game with the Los Angeles Angels of Anaheim on August 23, 2006 at Angel Stadium in Anaheim, California. (Photo by Stephen Dunn/Getty Images)
BOSTON - SEPTEMBER 12: Red Sox DH David Ortiz, right, hit a two run walk off ninth inning home run to lift Boston to a 5-4 victory over Tampa Bay. Here, as the fans go wild, he is mobbed at the plate by his teammates, including Curt Schilling, left, and Kevin Youkilis, center, as home plate umpire Greg Gibson, blue shirt, watches closely to make sure he steps on the plate. (Photo by Jim Davis/The Boston Globe via Getty Images)
BOSTON - OCTOBER 20: David Ortiz #34 of the Boston Red Sox looks on from the on-deck circle against the Cleveland Indians during game six of the American League Championship Series on October 20, 2007 at Fenway Park in Boston, Massachusetts(Photo by Rob Tringali/Sportschrome/Getty Images)
DENVER - OCTOBER 28: David Ortiz #34 of the Boston Red Sox celebrates with champagne in the locker room after winning Game Four by a score of 4-3 to win the 2007 Major League Baseball World Series in a four game sweep of the Colorado Rockies at Coors Field on October 28, 2007 in Denver, Colorado. (Photo by Jed Jacobsohn/Getty Images)
BOSTON - OCTOBER 30: David Ortiz #34 of the Boston Red Sox holds the World Series Trophy during the Boston Red Sox World Series Victory Celebration on October 30, 2007 in Boston, Massachusetts (Photo by Elsa/Getty Images)
BOSTON - APRIL 08: David Ortiz #34 of the Boston Red Sox connects with a pitch against the Detroit Tigers on April 8,2008 during Opening Day at Fenway Park in Boston, Massachusetts. (Photo by Elsa/Getty Images)
BOSTON - APRIL 29: David Ortiz #34 of the Boston Red Sox connects with a pitch during the MLB game against the Toronto Blue Jays on April 29, 2008 at Fenway Park in Boston, Massachusetts.The Red Sox defeated the Blue Jays 1-0. (Photo by Elsa/Getty Images)
ATLANTA - JUNE 28: First baseman David Ortiz #34 of the Boston Red Sox flips the ball towards first base during the game against the Atlanta Braves at Turner Field on June 28, 2009 in Atlanta, Georgia. The Braves beat the Red Sox 2-1. (Photo by Mike Zarrilli/Getty Images)
BOSTON - AUGUST 21: David Ortiz #34 of the Boston Red Sox shares a laugh with the New York Yankees during batting practice at Fenway Park on August 21, 2009 in Boston, Massachusetts. (Photo by Jim Rogash/Getty Images)
LATE NIGHT WITH JIMMY FALLON -- Episode 86 -- Pictured: (l-r) Jimmy Fallon gets hitting tips from Boston Red Sox Designated Hitter David Ortiz on January 11, 2010 (Photo by Dana Edelson/NBC/NBCU Photo Bank via Getty Images)
BOSTON, MA - SEPTEMBER 28: Xander Bogaerts #2 and David Ortiz #34 of the Boston Red Sox present Derek Jeter #2 of the New York Yankees with a placard in honor of his last game on September 28, 2014 at Fenway Park in Boston, Massachusetts. Photo by Michael Ivins/Boston Red Sox/Getty Images)
CLEVELAND, OH - OCTOBER 4: David Ortiz #34 of the Boston Red Sox tips his hat to the fans after leaving the game during the sixth inning after swapping out for a pitch runner following a walk against the Cleveland Indians at Progressive Field on October 4, 2015 in Cleveland, Ohio. (Photo by Jason Miller/Getty Images)
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The 43-year-old Ortiz, recognized as the beloved "Big Papi" by baseball fans during his 14 seasons in Boston, was shot in the back Sunday night while visiting a nightclub in Santo Domingo.
Lopez said Ortiz underwent six hours of surgery. Doctors removed his gallbladder and part of his colon and intestines. Ortiz also sustained liver damage, he added.
"Doctors say that David is out of danger, thank God," Ortiz's father, Leo Ortiz, told ESPN. "What they have told me post-op is that the doctors believe he will recover quickly."
His father added: "Big Papi will be around for a long time."
Police said Ortiz was shot at nearly point-blank range by a man identified as Eddy Feliz Garcia, 25. Ney Aldrin Bautista Almonte, the director of the Dominican National Police, said a group of people at the bar surrounded the suspect and beat him before police arrived, per ESPN.
Garcia was treated at a local hospital and released to police.
Police said it is unclear whether Ortiz was targeted.
Two others also were wounded in the attack.
Jhoel Lopez, a Dominican television host, was shot in the leg, and his injuries were not considered life-threatening. Police did not detail the injuries to the third person or make an identification.
The news of the shooting brought an outpouring of support on social media Monday morning, many of them remembering the role Ortiz played in helping the city to recover from the Boston Marathon bombing in 2013.
From former President Barack Obama: "Six years ago, David Ortiz's spirit and resolve helped us all begin to heal from the Boston Marathon bombing. Today, I want to join many others in wishing him a speedy recovery of his own. Get well soon, Papi."
From New England Patriots quarterback Tom Brady: "Papi defines Boston Strong... get well soon my friend!!!"
Ortiz ended his 20-year big league career in 2016, when he earned the last of his 10 All-Star appearances. The former designated hitter and first baseman won seven Silver Slugger awards in his career, and he hit 541 home runs with 1,768 RBIs in 2,408 games in the majors. He ranks 17th in major league history in career home runs.
Ortiz began his major league career by playing six seasons for the Minnesota Twins (1997-2002), but his career blossomed after he joined the Red Sox. 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.
He also helped the Red Sox win championships in 2007 and 2013, capturing World Series MVP honors in the latter season.