"I'm sorry, I'm sorry I couldn't do anything," Rodman told media on his arrival at Beijing airport from a weeklong trip. "It's not my fault. I'm sorry. I just want to do some good stuff, that's all I want to do."
He said he would return to North Korea next month, but gave no details.
Rodman and the squad of retired NBA players he took to North Korea for an exhibition game marking Kim's birthday have met with criticism in the U.S. because of North Korea's human rights record and its development of nuclear weapons.
Acknowledging the controversy surrounding the Rodman trip, one of the players, Charles D. Smith, said: "He opened the door and he did some missteps along the way."
In an interview in Beijing, Smith said Rodman's singing of "Happy Birthday" to Kim before the exhibition game at a Pyongyang stadium was something that he alone had decided to do. "I think that it might not have been the right thing to do, but he did it ... if it was done in private it would be different, but when it's done in the open like that, people are going to have opinions."
During the trip, Rodman was also slammed for not using his influence with Kim to help free Kenneth Bae, the missionary in poor health who has been detained for more than a year for "anti-state crimes." Rodman apologized last week for comments he made in a CNN interview implying Bae was at fault, saying he had been drinking and was upset because some of his teammates were leaving under pressure.
Smith said that the controversy surrounding Bae was a "bad situation" that "overshadowed some of the things that we were doing."
"Dennis is not a member of the State Department, he is not a member of the U.N.," Smith said. "For them to put the flag in his hands and say go and negotiate and talk about it, he probably would have made it worse, you know."
He said North Korean officials had invited the team back "at any given time."
On Monday, Rodman reiterated that his trip was one of goodwill.
"This is not a bad deal," he said. "I want to show people that no matter what's going on in the world, for one day, just one day, no politics, not all that stuff.
"I'm sorry for all the people and what's going on, I'm sorry," he continued. "I'm not the president, I'm not an ambassador, I'm just an individual that wants to show the world the fact that we can actually get along and be happy for one day."
Rodman and Kim struck up a friendship when the basketball-player-turned-celebrity first traveled to the secretive state last year.
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