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 Thursday through a publicist in an email message to The Associated Press.
In a CNN interview Tuesday, Rodman had an outburst about Bae, who was detained in North Korea in Nov. 2012 and placed in a labor camp. In the interview, Rodman was challenged on why he is not using his connections with Kim to help Bae. Rodman suggested that Kim was right in detaining the 45-year-old missionary.
"The one thing about politics, Kenneth Bae did one thing. If you understand -- if you understand what Kenneth Bae did," said Rodman. "Do you understand what he did? In this country?"
In Thursday's statement Rodman said: "I want to apologize. 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."
North Korea has accused Bae of "hostile acts" and attempting to stir up a coup. Bae has since been transferred to a hospital after facing a series of health problems.
Bae's sister, Terri Chung, shot back in a statement in response to Rodman's earlier comments.
"Dennis Rodman could do a lot of good by advocating for Kenneth to Kim Jong-un, but instead he has decided to hurl outrageous accusations at my brother, insinuating that Kenneth has done something sinister," she said.
"He is clearly uninformed about Kenneth's case, and he is certainly not in any position to pass judgment on Kenneth Bae, who has never any hostile intentions against the DPRK," she added.
Rodman assembled Wednesday's basketball game for Kim's birthday as part of what he calls "basketball diplomacy." Kim, his wife and other senior officials and their wives watched from a special seating area as Rodman sang "Happy Birthday." Rodman said he was honored to be able to play the game, and even called it "historic."
"It is clear to me, however, that there is nothing diplomatic about his trip. My family and I are outraged by Rodman's recent comments. He is playing games with my brother's life. There is no diplomacy, only games, and at my brother's expense," Chung said.
The U.S. has criticized Rodman's trips to North Korea as ill-advised and naive. Officials have also criticized the basketball game because of North Korea's human rights record, its development of nuclear weapons and its threats to use them if a conflict breaks out with Washington or Seoul.
ABC News and the Associated Press contributed to this report.