The 32-year-old prince is “worried about Ms. Markle’s safety and is deeply disappointed that he has not been able to protect her”, an official statement said.

“It is not right that, a few months into a relationship with him, Ms. Markle should be subjected to such a storm,” the statement said, adding that “the past week has seen a line crossed”.

Markle describes herself as mixed race, and has written online about racism experienced by her African American mother.

Writing for Elle magazine last year, she said she took “pride in being a strong, confident mixed-race woman”.

Markle said she often reluctantly tells people: “My dad is Caucasian and my mom is African American. I’m half black and half white.”

Daughter of a clinical therapist mother and television lighting director father, she grew up in Los Angeles, studied at a girl’s Roman Catholic high school before attending Northwestern University in Illinois. “My mother raised me to be a global citizen, with eyes open to sometimes harsh realities,” she said on her blog, thetig.com. Markle recalled how her mother imparted the lesson.

“I must have been about 10 years old when we visited the slums of Jamaica.” I had never seen poverty at that level and it registered in my glazed brown eyes. ‘Don’t look scared, Flower,’ she said. ‘Be aware, but don’t be afraid.’”

Best known as paralegal Rachel Zane in Suits, Markle has appeared on General Hospital, CSI: Miami, Without a Trace and Castle.

My Life: Meghan Markle

She also is an active campaigner on the subject of gender equality. Her activism started young: At 11, she wrote then-first lady Hillary Clinton to protest a soap company ad, complaining that it implied women belonged in the kitchen.

Markle and Harry reportedly met while the prince was in Canada promoting the Invictus Games, a sporting event for injured service personnel.

British media have published dozens of stories about Markle since rumours began circulating around early November that she was Prince Harry’s girlfriend.

The Sun, one of Britain’s most popular tabloids, ran a story last week under the headline “pushy princess”, publishing many family photographs and quoting Markle’s half-sister as saying the actress was “shallow” person driven by “social climbing”.

The Daily Mail, Britain’s biggest tabloid by combined online and print circulation, said it had commissioned a US genealogist to investigate the ancestry of Markle’s family, which is mainly white.

It said she came from “a family whose roots in the American South tell much of the struggle of the United States to come to terms with the legacy of slavery, and the divided society which grew up in its aftermath”.

A third tabloid, The Daily Mirror, ran a front-page story reporting that Markle “features on X-rated Pornhub website in steamy TV scenes”.

The Mirror said the scenes on the popular pornographic website showed the actress in her “racy role” in the television legal drama Suits.

The royal statement said Harry was “aware that there is significant curiosity about his private life.”

“He has never been comfortable with this, but he has tried to develop a thick skin about the level of media interest that comes with it.

“He has rarely taken formal action on the very regular publication of fictional stories that are written about him and he has worked hard to develop a professional relationship with the media, focused on his work and the issues he cares about,” it said. “But the past week has seen a line crossed.”

Prince Harry has previously complained of “incessant” intrusions into his private life and appealed for more privacy.

“Everyone has a right to privacy,” he told the BBC’s Andrew Marr programme in May. “Sadly that line between public and private life is almost non-existent any more.”