(CNN) -- Former NBA star Dennis Rodman apologized Thursday for his much-criticized outburst about an American citizen imprisoned in North Korea, saying he was stressed out and had been drinking when he made the remarks on CNN.
The family of that imprisoned American, Kenneth Bae, said Thursday that they accepted Rodman's apology for his "outrageous" remarks but said they hope his comments "have not further endangered" Bae.
The eccentric basketball veteran is in North Korea for a controversial visit that has been rife with bizarre moments, including Rodman's rendition of "Happy Birthday" to the country's leader Kim Jong Un at a packed sports stadium on Wednesday.
In an exclusive interview Tuesday with Chris Cuomo of CNN's "New Day," Rodman provoked outrage by appearing to suggest that Bae -- who has been held in North Korea since 2012 -- may have done something to deserve his sentence of 15 years of hard labor.
"I want to first apologize to Kenneth Bae's family," Rodman, 52, said Thursday in a statement released by his publicist Jules Feiler. "I want to apologize to my teammates and my management team. I also want to apologize to Chris Cuomo."
Bae's family had said they were shocked by Rodman's comments about the captive American.
"He was in a position to do some good and to help advocate for Kenneth," Bae's sister, Terri Chung, said Tuesday. "He refused to do so. But then instead he has chosen to hurl these outrageous accusations against Kenneth. He clearly doesn't know anything about Kenneth, about his case. And so we were appalled by that."
Rodman attributed his outburst to stress.
"I embarrassed a lot of people," said Rodman, who traveled to North Korea with other former NBA players for a basketball game against a North Korean team. "I'm very sorry. At this point I should know better than to make political statements. I'm truly sorry."
He said the day of the interview had been "very stressful."
"Some of my teammates were leaving because of pressure from their families and business associates," he said, adding that his dream of "basketball diplomacy was quickly falling apart."
"I had been drinking," he said. "It's not an excuse but by the time the interview happened, I was upset. I was overwhelmed."
In a written statement Thursday afternoon, Chung said the Bae family would accept his apology.
"As Rodman has stated, being drunk and stressed is not an excuse for what he said, but we acknowledge he is human and we all do make mistakes," the statement said. "Our greatest concern remains the health and freedom of my brother Kenneth. We hope and pray that Rodman's comments and ongoing antics have not further endangered my brother. Kenneth's health and freedom are precarious."
Human rights criticism
The NBA and the U.S. government have said they have nothing to do with Rodman's visit to North Korea, his fourth in less than a year. The Irish online betting company that had backed the trip withdrew its name from the venture last month after North Korea announced that Kim's once powerful uncle had been purged from his top government posts and executed.
Human rights activists have criticized Rodman for his chummy relationship with Kim and apparent unwillingness to address the North Korean regime's widely reported abuses against its impoverished population.
Rodman befriended Kim, an avid basketball fan who inherited power from his father, during his first North Korean visit last year and has described the young dictator as a "very good guy."
The two unlikely comrades appeared to be getting along famously at the basketball exhibition game Wednesday for Kim's birthday. The young leader, whose exact age is unknown, is believed to be in his early 30s.
"It was, as you might imagine, a bizarre and unusual occasion that won't easily be forgotten," Simon Cokerell, general manager of Koryo Tours, said in a YouTube video posted after he accompanied Western tourists to watch the event.
Birthday ball game
Accompanied by his wife, Kim emerged in the stadium in Pyongyang to cheering crowds who for several minutes wished him a long life, stopping only when the leader hushed them. Rodman gave an impromptu speech and then led the crowd in singing "Happy Birthday" to Kim.
Images released by The Associated Press also showed Rodman appearing to bow to Kim.
Rodman's squad and a North Korean team played two games, Cokerell said. In the first contest, the Americans lost to a North Korean squad, 47-39. The second game pitted squads with Western and North Korean players on each team.
"That game was actually much better; there was a lot of showboating, showing off, alley-oops, slam-dunks and that sort of thing," he said.
Rodman, who during his professional career set an NBA record for rebounds, didn't play the whole time, according to Sean Agnew, a tourist who said he had attended the unusual sporting event with Koryo Tours.
After participating for about 15 minutes, Rodman got changed and went to sit next to Kim in the audience, where the two spent the rest of the game smoking and laughing together, Agnew said.
"Kim Jong Un really seemed to be enjoying himself," said Agnew, who arrived in Beijing from Pyongyang on Thursday.
Next move uncertain
The next phase of Rodman's visit remained unclear Thursday. Feiler, the publicist, said he couldn't disclose when Rodman would return to the United States.
One of the other former NBA players involved in the game, Eric "Sleepy" Floyd, flew to Beijing on Thursday, but there was no sign of Rodman at the airport.
"It was fun, a lot of fun," Floyd said of the North Korean visit, before he was engulfed by a throng of journalists at the airport.
Agnew, who stayed in the same hotel in Pyongyang as Rodman's team, said he thought that the U.S. basketball players remaining in North Korea might be going skiing.
North Korean state-media recently published photos of Kim riding a ski-lift in a newly developed ski resort.
Outburst on CNN
Regardless of his next move, the shock waves from Rodman's bizarre performance during his CNN interview on Tuesday continue to reverberate.
Most striking were his comments on Bae, a Korean-American who was sentenced to 15 years of hard labor last year on charges that he planned an operation to topple North Korea's government through religious activities. The regime accused Bae of urging people to carry out "hostile acts" against the state.
Bae's family members say he is a devout Christian who ran a legal tour operation in North Korea but didn't fully understand the system there. His health has deteriorated during his detention and he was transferred to a hospital last year.
The U.S. government has repeatedly called on North Korea to grant Bae amnesty and release him.
But in his interview with CNN, Rodman intimated that Bae might have done something wrong without specifying what.
"Do you understand what he did in this country?" Rodman asked Cuomo. "No, no, no, you tell me, you tell me. Why is he held captive here in this country, why?"
"I would love to speak on this," Rodman said, before abruptly switching topic to talk about how his fellow basketball players had left their families behind to come to North Korea for the exhibition game.
Bill Richardson, a former U.S. ambassador to the United Nations who has visited North Korea, said Rodman had "crossed a line" in his comments about Bae.
Laura Ling, an American journalist who was imprisoned in North Korea for several months in 2009, said Rodman's remarks were "incomprehensible."
CNN's Stephanie Kotuby, Dave Alsup, Karl Penhaul, Michael Pearson, Laura Smith-Spark, Faith Karimi, Yuli Yang, Charlie Miller and Connie Young contributed to this report.