In a 1,000-word statement released in Korean, English and Japanese, management firm Big Hit Entertainment repeatedly offered its "sincerest apologies".

It sought to distance the septet from the row, saying it bore responsibility, and went on: "Big Hit does not condone any activities of war or the use of atomic weapons."

Responding to further accusations the K-pop stars had used Nazi imagery, the company said it opposed all organisations "oriented towards political extremism and totalitarian beliefs including Nazism".

Known for their boyish good looks, floppy haircuts and meticulously choreographed dance moves, BTS have become one of South Korea's best-known and most valuable musical exports.

They have sold 380,000 tickets for their current Japanese tour, and their singles sell hundreds of thousands of copies each.

But Koreans bitterly resent Tokyo's brutal 1910-45 colonisation of the peninsula, which came to an end with Japan's Second World War defeat after the atomic bombings of Hiroshima and Nagasaki.

Historical issues still weigh heavily on the relationship between the neighbours, both of them market democracies and US allies, even while they share widespread business and cultural connections.

Japanese television station TV Asahi last week cancelled a performance by BTS after a photo went viral of band member Jimin wearing the offending shirt.

The garment featured the phrase "PATRIOTISM OURHISTORY LIBERATION KOREA" repeated multiple times alongside an image of an atomic bomb explosion and another of Koreans celebrating their independence.

As the row escalated, images emerged of a concert last year where BTS wore uniforms and waved flags that critics said recalled Nazi symbols, and a 2014 photoshoot that shows leader RM wearing a cap bearing an SS Death's Head logo.

The SS played a key role in the Nazi mass murder of six million Jews during the Holocaust and a prominent Jewish human rights group accused the band of "mocking the past".

"It goes without saying that this group owes the people of Japan and the victims of Nazism an apology", said Rabbi Abraham Cooper of the Simon Wiesenthal Centre in Los Angeles.

"Those designing and promoting this group's career are too comfortable with denigrating the memory of the past," he added.

"The result is that young generations in Korea and around the world are more likely to identify bigotry and intolerance as being 'cool' and help erase the lessons of history."

In its statement, published on Facebook late Tuesday, Big Hit Entertainment said the performance in question was intended to criticise totalitarianism and was "in no way associated with National Socialism".

Rather, it said, it referred to a song "Classroom Idea", by veteran South Korean band Seo Taiji, which "levies social criticism against rigidly standardised education".