The former basketball star issued the apology through publicist Jules Feiler in an email message to The Associated Press, a day after he sang "Happy Birthday" to North Korean leader Kim Jong Un at the start of the friendly game.
Rodman has been slammed for not using his influence with Kim to help free Kenneth Bae, the missionary in poor health who is being confined in North Korea for "anti-state" crimes.
"I want to apologise," Rodman said today. "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."
Rodman said he wanted to apologise first to Bae's family. "I'm very sorry. At this point I should know better than to make political statements. I'm truly sorry."