He started to strangle her with a rope and Abargil thought she was going to die. But when he paused, she managed to convince him to let her go. She escaped with her life, and immediately reported it to the authorities.
The Italian police let him go due to a lack of evidence. But when she was back in Israel, the authorities issued an arrest warrant for Nur. He was tricked into returning to Israel and, after a lengthy trial, was sentenced to 16 years in prison.
At the time Abargil was crowned Miss World, the police investigation was on-going.
"When I stood on stage with the crown on my head, I think it was the first time that I realised what happened to me three months ago - and that I needed to go home immediately," she says. "I couldn't stay there for another minute. Going from the extreme of almost dying to being on that huge stage, with millions of people watching was, was too much.
"I wanted to die, basically. I didn't even care really. But God had different plans. I guess this crown was for me to do what I'm doing today. I'm travelling around the world and meeting amazing groups of men and women. As all Miss Worlds say, I wanted to save the world.
"Well, I took it seriously."
'Speak up about rape'
Today, Abargil is 34-years-old, a mother of three and a qualified lawyer. She's also a global advocate in the fight against sexual violence and has created a documentary, Brave Miss World, about her rape and subsequent activism. Since she was raped, she's been on a mission to 'save the world'. The film took four years to make, and in it, Abargil speaks to dozens of women who have also survived rape - including Hollywood stars Joan Collins and Fran Drescher.
It's now being shown at the Jewish Film Festival in the UK and is available on Netflix.
Most of the women she meets with have also shared their stories on her website 'Brave Miss World' where she encourages rape survivors to speak out. This is Abargil's main goal.
"I think it's very important to speak up. Because these women who don't speak, they don't want to believe it's happened. They're afraid to mention the word rape.
"If they say the word 'rape' they can shake all over and faint. It controls you. And for what? You let this person control you for the rest of your life.
"I think when you put what happened to you on the side, and you're not afraid to confront it, then you realise it's not what makes you who you are."
For Abargil, speaking out came naturally: "I wasn't like the other girls. I never blamed myself, or thought it happened because of me. I never kept it inside.
"At the time what I did felt normal. But now I realise that it wasn't. Because most victims don't speak, ever. I'm quite unique in that way. I speak, I shout, I'm not afraid."
'I hope men won't act like animals'
Reporting rape is an incredibly difficult process. And, as Abargil discovers in the film, not every woman has that option.
An American student at Princeton University relays her experience: "He came in, locked the door, turned off the lights, pushed me down on the floor and I kind of froze after a while and let him do whatever.
"[The university] said if I wanted to press charges I could, but it would probably be more painful for me than it would be for him. I thought I'd be seen as going away from the wishes of the school."
Abargil says: "I don't think everybody can [report it], they don't all have the support system. But I'm saying everyone should speak out to the people that can give them love, because love cures everything. If you know you can fall back on the people you love and they'll be there for you, it's worth everything."
Her hope is that by speaking out about the reality of rape, we will see a global change in the way society views sexual assault.
"Nothing will change if you don't speak. How can it? Reality changes laws.
"I hope men will be afraid because they know we're going to talk. I hope men are going to be men, and act like normal human beings, and not like animals. I hope that we're going to raise kids who respect themselves and other people."
She also hopes that women will start to change the way they view rape. That survivors will be able to speak about it, without any shame or stigma.
Women should stop hating themselves
"Women should stop hating themselves, because we hate ourselves in general. If something like this happens to us, we're the ones we blame. We're raised in a society where, if something doesn't go right, you're wrong. We have to be perfect.
"Instead of looking at us like a victim [people] look at us like we're the problem - like we're the rapist and did something wrong. I think it's because we look at ourselves this way."
In Abargil's documentary, which is directed by Gregory Peck's daughter Cecilia, she goes on a personal journey of acceptance. After two years of therapy in order to deal with her own rape, the intensity of hearing so many other women's stories affected her.
"I thought I was going to save the world when I started. I thought it would be much easier," she says. "But it was too much. I started to think this world was evil again and everything was only bad.
"It felt like every girl I've met was raped. Every man I met I thought he was a rapist. I really thought the situation was much worse than I ever imagined. The worst horror movies aren't as bad as the stories as I heard. I saw women who were helpless - no one supported them."
We have to change our views on rape
One of the most harrowing stories Abargil hears is that of Joan Collins, the 81-year-old actress who told how she was raped as a virgin, and then went on to marry her rapist.
"Women do so many horrible things because of their shame," says Abargil.
"After many women saw the film they said, 'I married my rapist, too'.
"They said, 'I felt like I was worth nothing. I thought he was the only one who's going to stay with me after what happened'.
"We have so much work as women to change the way society looks at rape, and the way we look at ourselves."
It's why, above all, Abargil's message is to rape survivors. She wants to talk directly to them and help them realise that they are not alone, and that there are people out there who want to help.
She ends with a message for them:
"You're still here and there's a reason for that. You can go to bed and cry all day but that won't take you anywhere. It will take you lower. Just put your head up and smile, even sometimes you don't feel like it. It stays and becomes real, in time.
"I really saw meeting all these amazing women that if you want to help yourself, no one else can help you - not even the people who love you the most. You have to help yourself."
