THERE are two types of people who respond passionately when they see the name "Batsheva" on a dance programme.

One group gets excited because they're dance fans and Batsheva – whether it's the parent company, or the youth wing known as Batsheva Ensemble – is a byword for brilliant choreographic invention and astounding technique. The other cadre of devoted followers is politically motivated: for them, "Batsheva" is a cue to stage anti-Israel protests outside venues – or indeed, as happened at this year's Edinburgh International Festival, inside the auditorium during a performance.

The morning after that opening night, Batsheva's artistic director Ohad Naharin was impressively philosophical about the disruptions. The voice is low, gravelly but soft. "It just makes me sad, what happened yesterday. Not for me – but for the dancers. For all of us, actually. All eight billion of us, because right now we are too busy with old ideas to look for new solutions. But I'm optimistic. I really am. I connect optimism to logic and logic tells me that there will be new solutions. Eventually."

In the meantime? He's succinct and frank. "There is injustice in the situation, and there is a government that is stalling. This is not a matter of opinion, it's a matter of reality."

He would have been willing to say all this to the pro-Palestinian protesters outside the Playhouse, and to listen to them, because he believes in dialogue offstage as well as on. Indeed, he'd been on the pavement, smoking a pre-performance cigarette and watching events, but apparently nobody recognised the lean, casually dressed man with the intense, observant gaze. If they had, and if they had engaged him in debate, they would have found Naharin prepared to talk politics, but more inclined to talk about art and how he consistently distances the multi-national Batsheva and his choreography from any notion that they represent an Israeli movement style, physical or political.

He's nailed that idea time and again in interviews, saying "there's a fine line between nationalistic feelings and pride. Pride can be a very dangerous thing. I care about loving to dance, not being proud to dance."

Back in 1990, however, necessity was the driving force behind the creation of Batsheva Ensemble. Naharin had just come into post as artistic director, but before he could put any plans into action there was a box that had to be ticked. He explains that "doing schools performances was a required element in our funding. To do that properly, seriously, we decided to form a separate company with its own repertoire – work that was interesting but also fun. But then it became a training place for dancers who joined Batsheva. It began as just five or six people, now there are around 20 dancers (aged between 18 and 24) and it's a full-time company, touring not just to schools but everywhere. So yes, now I have not one but two companies to enjoy."

That Naharin truly does enjoy the twin strands of Batsheva becomes more and more evident as he starts talking about time spent with them in the studio, making new work or just exploring ideas that surface during daily Gaga class. Gaga is the movement language he devised and which is now the training basis for both companies.

"Everything is shared," he says, "but yes, there is a difference. Ensemble dancers are younger but it's not entirely to do with age. Some young dancers can be very mature, some older dancers..." The pause, the twinkle in the eye, the smile says it all. Naharin himself turned 60 this summer, but when he's in the grip of an enthusiasm – leaning in, words flowing like warm, articulate molasses – he's like a wise kid, caught up in all the possibilities of a moment.

That feeling persists when he describes the studio as a playground, a place where Gaga encourages everyone to get under their own skin, discover not just strengths but weaknesses – and then draw on those perceived weaknesses to inform the humanity, the delicate details of temperament and experience, that give an inimitable colour and potency to Naharin's choreographies and Batsheva performances.

"In the studio, with the dancers, this is where I can be at my best," he says. "It is my school, where I learn and choreograph, and where I teach what I learn. And I do learn from looking at the dancers, seeing how they take Gaga into their bodies and also their minds, their imaginations. Use it to release unknown potential. Gaga is a very friendly language. It's not there to abolish what they already know, or to replace it. Gaga is a tool box. It's there to open up someone's talent. To enlarge the pleasure you can get from dancing by discovering what lies beyond the everyday routine – and for someone who comes into the Ensemble, maybe just fresh from high school and new to being part of a professional company... it is, really, remarkable to watch what they bring to that process of discovery.

HE adds: "Even when they doubt their abilities, or challenge the process, is interesting – actually, that can be the most inspirational moment for me. It opens up something new, something fresh."

When Batsheva Ensemble arrive at Edinburgh's Festival Theatre next week, they'll be performing Naharin's Deca Dance, a collage of extracts from various existing works. The mix changes, as does the running order, simply because Naharin likes the surprise that lurks in shaking things up and disrupting any cozy complacency. Which brings us back to the possibility of protests when the Ensemble are in town. "These dancers come from all over the world," he says. "They are artists, not politicians. Dance is about what unites us, and that has to do with human values, skill, passion and the power of imagination."

Batsheva Ensemble are at Edinburgh's Festival Theatre on Tuesday and Wednesday