US Airways was forced into a humiliating apology on Monday night after it posted an obscene pornographic image on Twitter in response to a customer.

The American airline tweeted the explicit image to an unhappy customer by mistake – but it took the firm nearly an hour to remove the post.

The pornographic image, which depicted a naked woman and a model plane, was included in a response to a customer who complained about her delayed flight from North Carolina to Oregon. The picture was accompanied by the message: "We welcome feedback, Elle. If your travel is complete, you can detail here for review and follow up."

The image was quickly retweeted around the world, spawning dozens of spin-off jokes and – eventually – an apology from US Airways.

The airline said in a statement: "Unfortunately the image was inadvertently included in a response to a customer. We immediately realised the error and removed our tweet.

"We deeply regret the mistake and we are currently reviewing our processes to prevent such errors in the future."

The airline, which has 422,000 followers on Twitter, said it had tried to flag the graphic image as inappropriate after it was tweeted to its account by another user.

The slip came just hours after a 14-year-old Dutch girl was arrested after tweeting a terror threat as a "joke" to American Airlines. The girl was detained by police in Rotterdam on Monday over the hoax tweet, in which she claimed she was a member of al-Qaida and would "do something really big" on 1 June.

The airline immediately responded to the girl to say it "takes these threats very seriously" and would pass her details to the FBI. The girl, known only as Sarah, panicked and replied: "I was joking and it was my friend not me, take her IP address not mine. I'm so scared I'm just a 14-year-old white girl I'm not a terrorist."