Looking for Layla

"You have your mother’s smile, an American smile," her scores of Iraqi relatives tell the 32-year-old before proudly drawing attention to the fact that she has "her father’s fine nose". The large eyes - dark as bitter chocolate - are another giveaway, of course. For Raffo is the daughter of a Catholic-Iraqi-Arab father and an American-Irish-Catholic mother.

Now, like many artists forged in America’s melting pot, she has set out to draw aside the veil of mystery that divides her two cultures. "Both the first Gulf War and the current conflict are imprinted on my psyche," she says. "I feel so split as an American and an Iraqi."

A decade ago, the University of Michigan graduate backpacked alone around Europe, hungry for "life". After one month of waiting patiently in Turkey, she made it to Baghdad and met her Iraqi family again - almost 20 years after she first went there with her parents as a toddler in 1974. Her first play, Nine Parts of Desire, which premieres at the Traverse before a London run at the Bush Theatre, is the result of her momentous 1993 journey. "That trip was my coming of age," she says.

Her powerful drama, in which she plays nine women, takes its title from a quote about Fatima, daughter of the prophet Muhammad: "God created sexual desire in ten parts; then gave nine parts to women and one to men."

The play explores the lives and desires of some of the women Raffo met. They range from wives and mothers to artists and doctors, through to the exiled and the bereaved, she says, showing me family photographs of her civil engineer father, George, as a boy, with his nine brothers and sisters in Musil, and the Catholic church where his father and grandfather carved the intricate marble decorations.

The faded, creased black-and-white photographs were gifts from her Iraqi family. "People are always wanting to give you things. If you admire a painting in someone’s house, they will take it down and give it to you, but I wanted only old pictures of my father and his family."

We meet in New York a few days before I sit in on afternoon rehearsals for Raffo’s play. She apologises that she’s still finding each character’s "dance", then proceeds to throws herself around the SoHo rehearsal space with fearless abandon, playing first the rejected wife, then the anguished doctor dying of cancer after exposure to depleted uranium - "that weapon of mass destruction". Now, she’s a grieving mother reciting her children’s names in a moving litany of the dead as she relates how their nine tiny, charred bodies were found fused together after a bombing raid.

In post-war Baghdad, Raffo made a profound journey into the hearts and minds of her father’s land and its people. Her Iraqi family had missed her with such a longing that they were not afraid to tell her repeatedly how much they needed and loved her, she says. She also met some extraordinary women - poets, artists, professionals - that she felt were "as old as Babylon and as beautiful as Sumerian goddesses".

"These women just aren’t in the world. There are no images of Iraqi women out there that aren’t flat, one-dimensional and somewhat victimised. The real Iraqi woman does not exist in western culture. When I returned to the US, people would say, ‘Oh, you’re an Arab - and you went to Baghdad, so did you wear a veil?’ That’s when I knew I had to tell the stories I’d heard because they’re funny, sexy, radical and deeply emotional."

In Nine Parts of Desire, Raffo is not veiled. She has one prop, though, an abeya, the all-enveloping black garment that Iraqi women wear. It’s almost another character in the play, becoming a cloak, a baby, dead children, a shroud and, in a thrilling coup de theatre, a painting.

The genesis of the play is that painting, which Raffo found in the Saddam Arts Centre in Baghdad.

"It was like being in the Museum of Modern Art in New York - if you can imagine that filled with floor-to-ceiling portraits of Saddam Hussein. Then I went upstairs into this little back room and there was a wonderful nude of a woman, standing with her back towards the viewer amid a thicket of bare trees. I was transfixed because I thought, ‘It’s a painting of me’.

"It spoke to me of femininity and of sorrow, everything I had felt in Iraq," says Raffo, offering a colour photocopy of the work by Iraqi artist Layla Attar.

"I found so much of myself in that painting. I immediately photographed it. When I got the film back it was the only picture that had come out on that roll of film. I’ve lived with that image ever since. I knew Layla had to be a character in my play, so I asked everyone if they knew her or her work. I tried so hard to meet someone that had met her but she kept slipping through my fingers like a shadow."

Raffo eventually discovered that Layla’s sister lives in London. "I do lots of TV commercials - young mums, that sort of thing. It pays the rent. I was booked to make an ad in London, so I thought I would definitely get to meet Layla’s sister. I ended up staying for more than a month, always trying to meet her through the Iraqi community, but whenever I phoned her there was no answer. Yet, every few days I met the most incredible Iraqi women.

"I went from womb to womb, being fed and housed and making deep friendships, but I never met her sister, although I gathered opinions about Layla and her work from people who either knew her or had seen her paintings. Now, my Layla character has morphed into someone else entirely in the play, although I use the image of her nude self-portrait in the piece."

Originally, Raffo intended to tell a Frida Kahlo-like story of a woman artist and her life. "Although I started interviewing women about Layla, now the play celebrates them. All their stories bleed into each other. Halfway into our interviews each woman would start telling me her own life story and that story might be utterly harrowing or truly inspiring.

"I found vulnerable women, strong women. So, I think Nine Parts of Desire could be called Looking for Layla ... but finding all these other women."

Layla Attar is dead. Her house was bombed during the first Gulf War and she survived, only to die at the age of 51 in the Clinton administration’s 1993 bombing raids. Much of her work was also destroyed. She had been curator of the Saddam Arts Centre, so the exhibit Raffo saw was staged in her memory. "There are endless questions about Layla. Was her work looted and destroyed after this war? How was she seen by the people? Was she perceived as a representative of Saddam’s regime? I have so many questions but I hope this play offers some answers about how women survive the terrible, painful burden of war."

• Nine Parts of Desire, Traverse Theatre, Edinburgh, 31 July-23 August.