Former NBA star Dennis Rodman apologised Thursday for his televised outburst about a US missionary detained in North Korea, explaining that he had been stressed and drinking at the time.

Rodman was roundly criticised for his angry tirade in an interview with CNN, in which he appeared to suggest that the missionary, Kenneth Bae, had merited the prison sentence of 15 years handed down last year.

"I want to first apologise to Kenneth Bae's family," Rodman said in a statement released Thursday by his publicist and cited by CNN.

"I embarrassed a lot of people," said Rodman, who was in the North Korean capital for an exhibition basketball match he had organised to mark the birthday of North Korean leader Kim Jong-Un.

"I'm very sorry. At this point I should know better than to make political statements. I'm truly sorry."

Bae's family said later in a statement that they accepted Rodman's apology for the "outrageous" TV outburst but also hit back, saying their loved one's plight was "not a game".

The statement issued by Bae's sister, Terri Chung, poured thinly-veiled scorn on Rodman's explanation.

"Our family accepts Dennis Rodman's apology for his outrageous outburst... 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," it said.

"We hope and pray that Rodman's comments and ongoing antics have not further endangered my brother. Kenneth's health and freedom are precarious.

"The fact is Kenneth's life is on the line. Though we understand Rodman enjoyed some laughs and smokes during a couple of basketball games in North Korea, to our family, this situation is no joke.

"This is not a game," added the statement by Chung, a professor based in Seattle.

Rodman's trip to North Korea along with a handful of other former NBA players has courted controversy, with accusations of pandering to a totalitarian regime with a terrible record on human rights.

Birthday tribute

At the exhibition match on Wednesday, Rodman had sung Happy Birthday to his "best friend" Kim who was watching the game in a packed Pyongyang auditorium.

Tourists who attended the game said Rodman's performance was akin to Hollywood sex symbol Marilyn Monroe famously serenading John F. Kennedy with a sultry version of the same song at a Democratic Party fundraising soirée in 1962.

"It was a little Marilyn Monroe to JFK, the tone of it," American college student Sophia Sokmensuer told reporters Thursday at Beijing airport.

"It was kind of Marilyn Monroe-ish," agreed Hakan Sokmensuer, Sophia's father.

"It started very slowly 'Happy...' and he put his arms up. And the Koreans had no idea," he told AFP.

It was Rodman's fourth trip to North Korea in 12 months and he has been criticised for failing to raise human rights issues or the plight of Bae.

In his statement Rodman said the day of the CNN 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."

Bae, a 45-year-old tour operator, was arrested in November 2012 as he entered the northeastern North Korean port city of Rason.

North Korea described Bae as a Christian evangelist who smuggled inflammatory material into the country and sentenced him to 15 years' hard labour for allegedly seeking to topple the government.

Asked in the CNN interview if he would use his influence with Kim Jong-Un to make the case for Bae's release, Rodman had said: "I don't give a rat's ass what the hell you think."

Rodman played in the first half of Wednesday's exhibition game before changing out of his basketball gear and joining Kim in the stands, where they chatted and smoked together.

Kim just last month oversaw the execution of his powerful uncle and political mentor Jang Song-Thaek on charges of treason and corruption.