A day after the former basketball star sang "Happy Birthday" to North Korean leader Kim Jong Un and led a squad of former NBA players in a friendly game, Rodman issued the apology through publicist Jules Feiler in an email message to The Associated Press.
"I want to apologize," Rodman said. "I take full responsibility for my actions. It had been a very stressful day. Some of my teammates were leaving because of pressure from their families and business associates. My dreams of basketball diplomacy was quickly falling apart. I had been drinking. It's not an excuse but by the time the interview happened I was upset. I was overwhelmed. It's not an excuse, it's just the truth.
"I want to first apologize to Kenneth Bae's family. I want to apologize to my teammates and my management team. I also want to apologize to Chris Cuomo. I embarrassed a lot of people. I'm very sorry. At this point I should know better than to make political statements. I'm truly sorry."
Rodman has been slammed for not using his influence with Kim to help free Bae, the missionary in poor health who is being confined in the North for "anti-state" crimes. On CNN on Tuesday, Rodman implied Bae was at fault.
Bae's sister, Terri Chung, said his family couldn't believe what Rodman said.
"Here's somebody who is in a position to do some good for Kenneth and refuses to do so," Chung told KOMO Radio in Seattle on Wednesday. "And then after the fact, instead, he decides to hurl these unqualified accusations against Kenneth. It's clear he has no idea what he's talking about. I'm not sure who he's talking to, where he's getting his information, but he's certainly no authority on Kenneth Bae."
The U.S. State Department distanced itself from Rodman and said it did not want to "dignify" his activities or comments in Pyongyang by commenting on them. But spokeswoman Jen Psaki said the department was open to speaking with Rodman on his return.
"We have not reached out to him. We've said before, if he wants to reach out to us, we're happy to hear from him and what he has to say," she told reporters.
Rodman dedicated the game to his "best friend" Kim, who along with his wife and other senior officials and their wives watched from a special seating area. The capacity crowd of about 14,000 at the Pyongyang Indoor Stadium clapped loudly as Rodman sang a verse from the birthday song.
Rodman said he was honoured to be able to play the game in the North Korean capital and called the event "historic." Some members of the U.S. Congress, the NBA and human rights groups, however, say he has become a public relations tool for North Korea's government.
The government's poor human rights record and its threats to use nuclear weapons against rival South Korea and the United States have kept it a pariah state. Kim shocked the world in December by having his uncle, once considered his mentor, executed after being accused of a litany of crimes including corruption, womanizing, drug abuse and attempting to seize power.
The 52-year-old Rodman has refused to address those concerns while continuing to forge a relationship with Kim, whose age has never been officially disclosed. The government did not say how old he turned Wednesday but he is believed to be in his early 30s.
At the start of the game, Rodman sang "Happy Birthday" to Kim, who was seated above in the stands at the stadium, and then bowed deeply as North Korean players clapped.
To keep it friendly, the Americans played against the North Koreans in the first half, but split up and merged teams for the second half.
The North Korean team scored 47 points to 39 for the Americans before the teams were mixed. Rodman played only in the first half and then sat next to Kim during the second half.
"A lot of people have expressed different views about me and your leader, your marshal, and I take that as a compliment," Rodman told the crowd. "Yes, he is a great leader, he provides for his people here in this country and thank God the people here love the marshal."
Rodman is the highest-profile American to meet Kim. He has carefully avoided getting involved in overtly political activities, saying that he is not a statesman and instead is seeking only to build cultural connections with the North through basketball that may help improve relations between Pyongyang and Washington.
The game is a new milestone in Rodman's unusual relationship with Kim, who inherited power after the death of his father in late 2011 and rarely meets with foreigners. He remains a mystery to much of the outside world and until recently, his birthday was also not widely known, though it was quietly observed elsewhere around the capital Wednesday.
Along with Rodman, the former NBA players included ex-All Stars Kenny Anderson, Cliff Robinson and Vin Baker. Also on the roster were Craig Hodges, who currently serves as head coach of the Halifax Rainmen in the National Basketball League, Doug Christie, Charles D. Smith and four streetballers.
Smith said he and the other players did not join Rodman in singing the birthday song.
"We always tell Dennis that he can't sing. He is tone deaf," Smith said. "He did it alone."
Associated Press writer Doug Esser in Seattle, Washington, contributed to this report.