(Reuters) - Director Cameron Crowe defended his decision to cast Caucasian actress Emma Stone as a part-Asian woman in his film Aloha, but apologised for offending viewers who said the role should have gone to an actor of Asian-Pacific heritage.

Crowe acknowledged the critiques in a statement posted on his website on Tuesday, saying he offered "a heart-felt apology to all who felt this was an odd or misguided casting choice."

Many critics had questioned the decision.

Entertainment Weekly's Chris Lee wrote: "Accepting Emma Stone as an Asian-American in Aloha requires a certain suspension of disbelief."

Crowe had defended his casting choices for the Hawaii-based movie well before its May 29 release after it came under fire for its Caucasian-led cast, particularly Stone's role as an Air Force fighter pilot who is one quarter Hawaiian and has a half-Chinese father.

But he said he purposefully chose the green-eyed, strawberry-blonde actress to match the character of Allison Ng, who was based on a red-headed Hawaiian native.

"Captain Allison Ng was written to be a super-proud one-quarter Hawaiian who was frustrated that, by all outward appearances, she looked nothing like one," Crowe wrote on his blog on Tuesday.

"Extremely proud of her unlikely heritage, she feels personally compelled to over-explain every chance she gets."

The film has stumbled at the box office, having earned just over US$10.5 million (S$14.2 million) in North America, according to Box Office Mojo.

It has garnered a low 18 per cent approval rating on film review site RottenTomatoes.com.

Still, Crowe said he appreciates the opportunity to spark dialogue about diversity in Hollywood.

"Many of us are hungry for stories with more racial diversity, more truth in representation, and I am anxious to help tell those stories in the future," he said.

He said Aloha has "felt like a misunderstood movie". "It was a small movie, made by passionate actors who wanted to join me in making a film about Hawaii, and the lives of these characters who live and work in and around the island of Oahu," he wrote.